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Highlights of 2008/2009

Classical and Quantum Gravity

Cover image: Colour-coded TM reflectivity of a waveguide structure versus groove depth and waveguide thickness A Bunkowski et al 2006 Class. Quantum Grav. 23 7297–303.


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Dear Colleague,There has never been a better time to publish in Classical and Quantum Gravity (CQG). In 2009, CQG was awarded its highest ever impact factor of 3.035 and the journal continues to publish more and more exciting research from all areas of gravitational physics. As always, CQG offers the most rigorous peer review in the field with all papers being carefully appraised by 2 independent reviewers.

2010 is sure to be more exciting still. One of the most important recent developments has been the commissioning of special ‘Cluster’ issues, which are small, focussed, invitation-only issues of the journal targeting the best research in topical areas of gravitational physics. In 2010, CQG will present a cluster issue on Nonlinear Cosmological Perturbation Theory and a double-issue of selected Numerical Relativity and Relativistic Astrophysics content presented at the NRDA 2009 and MICRA 2009 meetings.

In this brochure, you may browse the abstracts of a selection of articles chosen by CQG’s Editorial Board in June 2009 as the CQG Highlights of the previous 12 months.

Each article can be found online at iopscience.org/cqg and will be free to download until 1 November 2010.

I’d like to take this opportunity to thank all of the authors and referees who give their support to CQG. I hope that you will consider CQG your first choice venue for publication of your next paper!

Editor-in-Chief Clifford M Will

Readership by regions in 2009

Full-text downloads

Impact FactoR

3.035** As listed in ISI®’s 2008 Science

Citation Index Journal citation reports

Image taken from: ‘Titania-doped tantala/silica coatings for gravitational-wave detection’ G M Harry et al 2007 Class. Quantum Grav. 24 405–15.

Images taken from: ‘A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild–anti de Sitter black holes’ R G Daghigh and M D Green 2009 Class. Quantum Grav. 26 125017.

Image taken from: ‘Simulating the emission and outflows from accretion disks’ S C Noble et al 2007 Class. Quantum Grav. 24 S259–S274.


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Journal ScopePublished twice monthly (24 issues per year), Classical and Quantum Gravity publishes original research articles on the subjects of gravitational physics and the theory of spacetime. The readership comprises gravitational theorists and experimentalists in physics, mathematics and cosmology.

Papers are published under the following areas:

•Classical general relativity

•Applications of relativity

•Experimental gravitation

•Cosmology and the early universe

•Quantum gravity

•Supergravity, superstrings and supersymmetry

•Mathematical physics relevant to gravitation

More information on each of these areas can be found at iop.org/cqg.

Contentspage

Topical Reviews 8

Fast Track Communications 8

Special issue articles 10

Regular papers 12

•Cosmology 12

•Experimental Gravity 14

•Mathematical General Relativity 15

•Numerical Relativity 16

•Black Holes 16

•Quantum Cosmology 17

•Quantum Gravity 19

•Strings, Branes, Supergravity, Gauge Theory 20

•Geometry, Topology 21

•Comments, Replies and Notes 22

Images taken from: ‘Quasinormal modes of black holes and black branes’ E Berti et al 2009 Class. Quantum Grav. 26 163001.


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Journal team

Publishing AdministratorJohn Fryer

Publisher Adam Day

Production Editor Vanessa Chesher

Publishing Editor Suzie Prescott

Marketing ExecutiveZoe Anderson

Editor-in-chiefC M Will, Washington University, St Louis, USA

L Andersson, University of Miami, USAV Balasubramanian, University of Pennsylvania, Philadelphia, USA A A Coley, Dalhousie university, Halifax, CanadaA Corichi, Universidad Nacional Autónoma de México (UNAM), Morelia, MexicoS Dhurandhar, Inter-University Centre for Astronomy and Astrophysics, Pune, India V P Frolov, University of Alberta, Edmonton, Canada D Garfinkle, Oakland University, Rochester, MI, USA G Gonzalez, Louisiana State University, Baton Rouge, USA J Isenberg, University of Oregon, Eugene, USA K Kuroda, University of Tokyo, JapanL Lehner, Louisiana State University, Baton Rouge, USA R B Mann, University of Waterloo, Ontario, Canada M Mars, Universidad de Salamanca, Spain P R L V Moniz, Universidade da Beira Interior, Covilhã, Portugal

B Mours, Laboratoire d’Annecy-le-Vieux de Physique des Particules, France S Mukohyama, IPMU, University of Tokyo, JapanN Ó Murchadha, University College Cork, Ireland E Poisson (Book Reviews Editor), University of Guelph, Guelph, Canada L Rezzolla, Max-Planck-Institut für Gravitationsphysik, Golm, Germany V O Rivelles, Universidade de Sao Paulo (USP), Sao Paulo, Brazil S F Ross, Durham University, Durham, UKC Rovelli, Université de la Mediterranée–Aix-Marseille II, France J Samuel, Raman Research Institute, IndiaM Sasaki, Kyoto University, Japan J M M Senovilla, Universidad del País Vasco, Bilbao, Spain C C Speake, University of Birmingham, Birmingham, UKD Sudarsky, Universidad Nacional Autónoma de México (UNAM), Morelia, MexicoR-S Tung, Shanghai Normal University, Shanghai, China D Wands, University of Portsmouth, UK

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Top 20 Most Downloaded articles from Vol 26 (2009)1 What is a particle? Daniele Colosi et al 2009 Class. Quantum Grav. 26 025002 (22pp)

2 Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project Benjamin Aylott et al 2009 Class. Quantum Grav. 26 165008 (51pp)

3 Local Hawking temperature for dynamical black holes S A Hayward et al 2009 Class. Quantum Grav. 26 062001 (8pp)

4 The double pulsar system: a unique laboratory for gravity M Kramer et al 2009 Class. Quantum Grav. 26 073001 (20pp)

5 The gravitational-wave signature of core-collapse supernovae Christian D Ott 2009 Class. Quantum Grav. 26 063001 (48pp)

6 The information paradox: a pedagogical introduction Samir D Mathur 2009 Class. Quantum Grav. 26 224001 (31pp)

7 The alternative to classical mass renormalization for tube-based self-force calculations Andrew H Norton 2009 Class. Quantum Grav. 26 105009 (19pp)

8 LISA Pathfinder: the experiment and the route to LISA M Armano et al 2009 Class. Quantum Grav. 26 094001 (18pp)

9 Quasinormal modes of black holes and black branes Emanuele Berti et al 2009 Class. Quantum Grav. 26 163001 (108pp)

10 Warped AdS3 black holes in new massive gravity Gérard Clément 2009 Class. Quantum Grav. 26 105015 (11pp)

11 Hamiltonian general relativity and the Belinskii–Khalatnikov–Lifshitz conjecture Abhay Ashtekar et al 2009 Class. Quantum Grav. 26 052001 (10pp)

12 The path to the enhanced and advanced LIGO gravitational-wave detectors J R Smith et al 2009 Class. Quantum Grav. 26 114013 (8pp)

13 On the resolution of the big bang singularity in isotropic loop quantum cosmology Madhavan Varadarajan 2009 Class. Quantum Grav. 26 085006 (21pp)

14 Lectures on holographic methods for condensed matter physics Sean A Hartnoll 2009 Class. Quantum Grav. 26 224002 (61pp)

15 The tensor-vector-scalar theory and its cosmology Constantinos Skordis 2009 Class. Quantum Grav. 26 143001 (43pp)

16 What is the entropy of the universe? Paul H Frampton et al 2009 Class. Quantum Grav. 26 145005 (7pp)

17 Gravity and hydrodynamics: lectures on the fluid-gravity correspondence Mukund Rangamani 2009 Class. Quantum Grav. 26 224003 (48pp)

18 Status of NINJA: the Numerical INJection Analysis project Laura Cadonati et al 2009 Class. Quantum Grav. 26 114008 (13pp)

19 A new proof of the Bianchi type IX attractor theorem J Mark Heinzle et al 2009 Class. Quantum Grav. 26 075015 (28pp)

20 Geodesics and symmetries of doubly spinning black rings Mark Durkee 2009 Class. Quantum Grav. 26 085016 (33pp)

http://iopscience.iop.org/0264-9381/26/2/025002





















8 H i g h l i g h t s 2 0 0 9

Karim A Malik and David R Matravers

2008 Class. Quantum Grav. 25 193001

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second orders, striking a balance between mathematical rigour and usability. In particular, we discuss gauge issues and the active and passive approaches to calculating gauge transformations. We also construct gauge-invariant variables, including the second-order tensor perturbation on uniform curvature hypersurfaces.

M Kramer and N Wex


The PSR J0737–3039 is a double neutron star system in which both stars are detectable as active radio pulsars. The pair, consisting of an old, mildly recycled 23-ms pulsar and a young 2.8-s pulsar, orbit the common centre of mass in a slightly eccentric, compact orbit with a short orbital period of 147 min. The combination of system parameters makes this binary pulsar the most relativistic binary pulsar known and allows unique tests of general relativity and alternative theories of gravity. Hence, we summarize the importance of the system for such tests, and pay attention, for instance, to the observed measurement of relativistic spin precession which confirms the ‘effacement’ property of a spinning body. We also present a method to use measurements of the absolute position angle of the linearly polarized radio emission of the pulsars to measure the rate of the relativistic spin precession. We demonstrate how spin–orbit coupling will eventually allow us to determine the moment-of-inertia of pulsar A, and provide a general outlook into the prospects of future observations of the double pulsar.

Eric A Bergshoeff, Mees de Roo and Olaf Hohm


We show that the Bagger–Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal theories in 2 + 1 dimensions. This leads to the Bagger–Lambert theory, with the embedding tensor playing the role of the four-index antisymmetric tensor defining a ‘3-algebra’. We present an alternative formulation of the theory in which the embedding tensor is replaced by a set of unrestricted scalar fields. By taking these scalar fields to be parity-odd, the Chern–Simons term can be made parity-invariant.

A concise introduction to perturbation theory in cosmology

The gravitational-wave signature of core-collapse supernovae

The double pulsar system: a unique laboratory for gravity

Multiple M2-branes and the embedding tensor

Highlighted topical Reviews

Highlighted Fast track communications

CQG publishes Topical Reviews in various areas of gravitational physics. The Reviews are carefully chosen and invited to the journal by the Editorial Board. They provide timely and authoritative information in areas where there has been significant recent progress. The Topical Reviews are among the most downloaded articles in CQG.

The exclusive Fast Track Communications section welcomes short, high impact submissions of strictly 8 pages or less. FTCs are among the most downloaded articles in CQG. FTCs are free to read for 10 years following publication.

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Figure 4. Colormap depicting the specific entropy distribution in the equatorial plane of the 20-M_ model s20A2B4 of Ott et al [42, 119, 115] at 90 ms after core bounce. Red and yellow regions of the PNS core have lowentropy (*1–3 kB baryon*1) while dark blue and black symbol-ize high entropy >6 kB baryon*1. The nonaxisym-metric structures are of primarily m = {1, 2, 3} nature with radial variations in dominance.

Christian D Ott


We present an extensive review of the ensemble of anticipatedgravitational-wave (GW) emission processes in stellar core collapse and postbounce core-collapse supernova evolution. Galactic core-collapse supernovae are very rare events, but within 3 5 Mpc from Earth, the rate jumps to 1 in ~2 years. Using the set of currently available theoretical gravitational waveforms, we compute upper-limit optimal signal-to-noise ratios based on current and advanced LIGO/GEO600/VIRGO noise curves for the recent SN 2008bk which exploded at ~3.9 Mpc. While initial LIGOs cannot detect GWs emitted by core-collapse events at such a distance, we find that advanced LIGO-class detectors could put significant upper limits on the GW emission strength for such events. We study the potential occurrence of the various GW emission processes in particular supernova explosion scenarios and argue that the GW signatures of neutrino-driven,magneto-rotational, and acoustically-driven core-collapse SNe may bemutually exclusive. We suggest that even initial LIGOs could distinguish these explosion mechanisms based on the detection (or non-detection) of GWs from a galactic core-collapse supernova.

Fast Track Communications

median receipt to first decision timesRegular papers

49 DaYSFTCs

30 DaYS






H i g h l i g h t s 2 0 0 9 9

István Rácz


A key result in four-dimensional black hole physics, since the early 1970s, is Hawking’s topology theorem assertion that the cross-sections of an ‘apparent horizon’, separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking’s argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking’s black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher

dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent.

Jörg Hennig, Marcus Ansorg and Carla Cederbaum


We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality 8π|J| < A holds, where J is the angular momentum and A the horizon area of the black hole.

Marcus Ansorg and Jörg Hennig


We investigate the interior of regular axisymmetric and stationary black holes surrounded by matter and find that for non-vanishing angular momentum of the black hole the spacetime can always be extended regularly up to and including an inner Cauchy horizon. We provide an explicit relation for the regular metric at the inner Cauchy horizon in terms of that at the event horizon. As a consequence, we obtain the universal equality (8πJ)2 = A+A− where J is the black hole’s angular momentum and A− and A+ denote the horizon areas of inner Cauchy and event horizons, respectively. We also find that in the limit J 0 the inner Cauchy horizon becomes singular.

Viqar Husain and Sanjeev S Seahra


We study the evolution of wormhole geometries under the Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a form of critical phenomena reminiscent of that observed in gravitational collapse. Similar results are obtained for initial data that describe space bubbles attached

to asymptotically flat regions. Our numerical methods are applicable to ‘matter-coupled’ Ricci flows derived from conformal invariance in string theory.

Geoffrey Compère and Stéphane Detournay


It is shown that the warped black hole geometries discussed recently in arXiv:0807.3040 (Anninos et al 2008) admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows us to find the central charge of the Virasoro algebra. The right-moving central charge

is obtained when the Virasoro generators are normalized in order to have a positive zero-mode spectrum for the warped black holes. If one normalizes the Virasoro generators in order to have a positive central charge, the zero mode is then unbounded from below. The current algebra is also shown to be centrally extended.

Abhay Ashtekar, Adam Henderson and David Sloan


The Belinkskii, Khalatnikov and Lifshitz conjecture says that as one approaches spacelike singularities in general relativity, ‘time derivatives dominate over spatial derivatives’ so that the dynamics at any spatial point is well captured by an ordinary differential equation. By now considerable evidence has accumulated in favor of these ideas. Starting with a Hamiltonian framework, we provide a formulation of this conjecture in terms of variables that are tailored to non-perturbative quantization. Our formulation serves as a first step in the analysis of the fate of generic spacelike singularities in loop quantum gravity.

A simple proof of the recent generalizations of Hawking’s black hole topology theorem

A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter

Ricci flows, wormholes and critical phenomena

Semi-classical central charge in topologically massive gravity

Hamiltonian general relativity and the Belinskii–Khalatnikov–Lifshitz conjecture

G )

( )C v l

35 3

R 2

2

=−+

+v(v

ˆˆ ˆ

Figure 1. The black hole, represented by the shaded region, is bounded by horizon H that is foliated by MOTS’ homologous to .

Figure 4. Embedding diagrams of 3-geometries representing a bubble connecting twoasymptotically flat regions.








10 H i g h l i g h t s 2 0 0 9

Daniel J Eisenstein


I review the observational evidence for dark energy, arguing that the large-scale structure observed at low redshift and in the cosmic microwave background offers a strong corroboration of the supernova Ia results. The angular scale of the acoustic oscillations in the cosmic microwave background strongly support a nearly flat universe, while many arguments from low-redshift cosmology support a matter density around 25% of the critical density. The observational constraints on the cosmological model have improved dramatically over the past decade. The coming decade will likely bring another two to three orders of magnitude in improvements in the data sets used for the study of dark energy.

Observing dark energy

Ralf Schützhold


The concept of a horizon known from general relativity describes the loss of causal connection and can be applied to non-gravitational scenarios such as out-of-equilibrium condensed-matter systems in the laboratory. This analogy facilitates the identification and theoretical study (e.g. regarding the trans-Planckian problem) and possibly the experimental verification of ‘exotic’ effects known from gravity and cosmology, such as Hawking radiation. Furthermore, it yields a unified description and better understanding of non-equilibrium phenomena in condensed-matter systems and their universal features. By means of several examples including general fluid flows, expanding Bose–Einstein condensates and dynamical quantum phase transitions, the concepts of event, particle and apparent horizons will be discussed together with the resulting quantum effects.

Emergent horizons in the laboratoryHighlighted Special issue articlesCQG seeks high quality articles of a common theme for special issues. CQG special issues differ from proceedings volumes in that all articles are peer reviewed to CQG’s usual high standards.

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R C Myers and S E Vázquez


In recent years, experiments have discovered an exotic new state of matter known as the strongly coupled quark–gluon plasma (sQGP). At present, it seems that standard theoretical tools, such as perturbation theory and lattice gauge theory, are poorly suited to understand this new phase. However, recent progress in superstring theory has provided us with a theoretical laboratory for studying very similar systems of strongly interacting hot non-Abelian plasmas. This surprising new perspective extracts the fluid properties of the sQGP from physical processes in a black hole spacetime. Hence we may find the answers to difficult particle physics questions about the sQGP from straightforward calculations in classical general relativity.

Quark soup al dente: applied superstring theory

R L Ward et al


The Laser Interferometer Gravitational Wave Observatory (LIGO) operates a 40m prototype interferometer on the Caltech campus. The primary mission of the prototype is to serve as an experimental testbed for upgrades to the LIGO interferometers and for gaining experience with advanced interferometric techniques, including detuned resonant sideband extraction (i.e. signal recycling) and dc readout (optical homodyne detection). The former technique will be employed in Advanced LIGO, and the latter in both Enhanced and Advanced LIGO. Using dc readout for gravitational wave signal extraction has several technical advantages, including reduced laser and oscillator noise couplings as well as reduced shot noise, when compared to the traditional rf readout technique (optical heterodyne detection) currently in use in large-scale ground-based interferometric gravitational wave detectors. The Caltech 40m laboratory is currently prototyping a dc readout system for a fully suspended interferometric gravitational wave detector. The system includes an optical filter cavity

at the interferometer’s output port, and the associated controls and optics to ensure that the filter cavity is optimally coupled to the interferometer. We present the results of measurements to characterize noise couplings in rf and dc readout using this system.

dc readout experiment at the Caltech 40m prototype interferometer

Figure 1. Phase diagram of QCD according to theorists [6]. The arrows show caricatures of theevolution of matter in typical RHIC collisions.

Figure 2. Sketch of the origin of Hawking radiation (red curves) in a de Laval nozzle.

Figure 2. The dc readout sensing chain. Visible on the table are one PZT steering mirror, themode-matching telescope, the output mode cleaner (made of copper to damp vibrational modes), the dc photodetectors and other optics.


http://iopscience.iop.org/0264-9381/25/11/114008?ejredirect=migration




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E Berti, V Cardoso, J A González, U Sperhake and B Brügmann


We present a preliminary study of the multipolar structure of gravitational radiation from spinning black hole binary mergers. We consider three different spinning binary configurations: (1) one ‘hang-up’ run, where the black holes have equal masses and large spins initially aligned with the orbital angular momentum; (2) seven ‘spin-flip’ runs, where the holes have a mass ratio q M1/M2 = 4, the spins are anti-aligned with the orbital angular momentum, and the initial Kerr parameters of the holes j1 = j2 = ji (where j J/M2) are fine-tuned to produce a Schwarzschild remnant after merger; (3) three ‘super-kick’ runs where the mass ratio q = 1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin–orbit and spin–spin terms in a multipolar decomposition of the post-Newtonian waveforms improves agreement with the numerical simulation.

Multipolar analysis of spinning binaries

C Anastopoulos and B L Hu


We investigate the meaning of gravity-induced decoherence in quantum theory, known as ‘intrinsic’ or ‘fundamental’ decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuations as the origin of intrinsic or fundamental decoherence: one that models the fluctuations by stochastic process and one that purports to derive decoherence from the quantum fluctuations of real clocks.

Intrinsic and fundamental decoherence: issues and problems

Valeri P Frolov and David Kubiznák


In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing–Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing–Yano 2-form) in 4D flat spacetime one can ‘generate’ the 4D Kerr–NUT–(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr–NUT–(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing–Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton–Jacobi, Klein–Gordon and Dirac equations in the general Kerr–NUT–(A)dS metrics.

Higher-dimensional black holes: hidden symmetries and separation of variables

S Carlip


In view of the enormous difficulties we seem to face in quantizing general relativity, we should perhaps consider the possibility that gravity is a fundamentally classical interaction. Theoretical arguments against such mixed classical–quantum models are strong, but not conclusive, and the question is ultimately one for experiment. I review some work in progress on the possibility of experimental tests, exploiting the nonlinearity of the classical–quantum coupling, which could help settle this question.

Is quantum gravity necessary?

N Dorey


In this paper, I review introductory aspects of integrability in the context of the AdS/CFT correspondence. The emergence of integrability and the resulting description in terms of factorized scattering are discussed both in one-loop gauge theory and in semiclassical string theory.

Integrability and the AdS/CFT correspondence

Vijay Balasubramanian, Jan de Boer, Sheer El-Showk and Ilies Messamah


Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In cases with enough supersymmetry, it has been possible to explicitly construct such microstates in spacetime and understand how coarse graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise in type II string theory on AdS

5 × S5 and on AdS3 × S3 × T4 that preserve 16 and eight supercharges, respectively. For such a picture of black holes as effective geometries to extend to cases with a finite horizon area, the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. By studying examples in M-theory on AdS

3 × S2 × CY that preserve four supersymmetries, we show how this can happen.

Black holes as effective geometries

Figure 2. Sketch of a three-centre attractor flow tree from [22, 35]. Lines with arrows indicate single-centre attractor flows while straight lines without arrows are walls of marginal stability. The tree starts at the circle on top (the moduli at infinity) and flows towards the attractor points

indicated by the boxes. Note here that Γ4 Γ1 Γ2 and Γ Γ4 Γ3. On the walls of marginal

stability the moduli are such that |Z(Γ; t)| |Z(Γ3; t)| |Z(Γ4; t)| (horizontal wall on top) and

|Z(Γ4; t)| |Z(Γ1; t)| |Z(Γ2; t)| (diagonal wall on bottom left).








12 H i g h l i g h t s 2 0 0 9

Bernard F Schutz


LISA has the potential to make observations that probe deeply into fundamental physics. Not only will it test to exquisite precision the general relativity model for gravitational radiation, but will also test strong-field gravity and in particular the proposition that all black holes are described by the Kerr metric. More research is needed, however, on how to quantify the theoretical meaning of any deviations that might be seen from general relativity. LISA can also make important contributions where cosmology and fundamental physics join. LISA’s observations of black-hole coalescences, out to redshifts of 20 or more, provide a completely new distance measure, one that needs no calibration and is independent of the standard cosmological ‘distance ladder’. Using this measure, LISA may even begin to measure or limit the time dependence of the dark energy equation of state. Beyond these expected results from LISA is the mission’s discovery space: LISA’s high sensitivity raises real possibilities that it will discover sources in the dark part of the universe that were completely unexpected.

Fundamental physics with LISA

Cyril Pitrou


This paper investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor-valued distribution function, we study the gauge dependence of the distribution function and summarize the construction of the gauge-invariant distribution function. The Liouville operator which describes the free streaming of electrons, and the collision term which describes the scattering of photons on free electrons are computed up to second order. Finally, the remaining dependence in the direction of the photon momentum is handled by expanding in projected symmetric trace-free multipoles and also in the more commonly used normal modes components. The results obtained remain to be used for computing numerically the contribution in the cosmic microwave background bi-spectrum which arises from the evolution of second-order perturbations, in order to disentangle the primordial non-Gaussianity from the one generated by the subsequent nonlinear evolution.

The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization

Silke Weinfurtner, Piyush Jain, Matt Visser and C W Gardiner


We investigate cosmological particle production in spacetimes where Lorentz invariance emerges in the infrared limit, but is explicitly broken in the ultraviolet regime. Thus these models are similar to many (but not all) models of quantum gravity, where a breakdown of Lorentz invariance is expected for ultraviolet physics around the Planck/string scale. Our specific model focuses on the boost subgroup that supports CPT invariance and results in a momentum-dependent dispersion relation. Motivated by previous studies on spacetimes emerging from a microscopic substrate, we show how these modifications naturally lead to momentum-dependent rainbow metrics. Firstly, we investigate the possibility of reproducing cosmological particle production in spacetimes emerging from real Bose gases. Several papers have been written on the analogy between the kinematics of linearized perturbations in Bose–Einstein condensates and effective curved-spacetime quantum field theory. Recently we have studied the influence of nonperturbative ultraviolet corrections in time-dependent analog spacetimes, leading to momentum-dependent emergent rainbow spacetimes. We show that models involving a time-dependent microscopic interaction are suitable for mimicking quantum effects in FRW spacetimes. Within certain limits the analogy is sufficiently good to simulate relativistic quantum field theory in time-dependent classical backgrounds, and the quantum effects are approximately robust against the model-dependent modifications. Secondly, we analyze how significantly the particle production process deviates from the common picture. While very low-energy modes do not see the difference at all, some modes ‘re-enter the Hubble horizon’ during the inflationary epoch, and extreme ultraviolet modes are completely insensitive to the expansion. The analysis outlined here, because it is nonperturbative in the rainbow metric, exhibits features that cannot be extracted simply from the standard perturbative modification of particle dispersion relations. However, we also show how the final result, after many e-foldings, will approach a time-independent exponentially decaying particle spectrum.

Cosmological particle production in emergent rainbow spacetimes

Figure 6. In this figure, we compare the quasi-particle production per quantum mode (left column) with its frequency ratio (right column), for ts 1 104. Parameters are C

NL( t 0) 1 105,N0 107 and X 2 103. The bold plotted dots on the left-hand side indicate that the frequency ratio is below one, hence the quantum mode corresponds to a super-Hubble horizon mode. While on the right-hand side we indicated with the bold dots when a change in the mode occupation number is above a certain threshold—here ∆Nk 0.004—to filter out quantum noise fluctuations. (a) Nk (t); (b) Rk (t); (c) Nk (t) projected onto the tNk plane; (d) Rk (t) projected onto the tRk plane; (e) Nk (t) projected onto the kNk plane; (f ) Rk (t) projected onto the kRk plane.

cosmology highlightsq

Highlighted Regular papersCQG is primarily an original research journal publishing novel and interesting original research papers in all areas of gravitational physics. All articles are peer reviewed to CQG’s usual high standards by 2 independent referees. A selection of top original research papers chosen by the CQG Editorial Board makes up the majority of the CQG Highlights.

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H i g h l i g h t s 2 0 0 9 13

H R Sepangi, B Shakerin and B Vakili


We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum regimes. The phase-space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain some approximate analytical solutions for the corresponding classical and quantum cosmology in the presence of the deformed Heisenberg relations between the phase-space variables, in the limit where the

minisuperspace variables are small. These results are compared with the standard commutative and noncommutative cases, and similarities and differences of these solutions are discussed.

Deformed phase space in a two-dimensional minisuperspace model

Tsuyoshi Houri, Takeshi Oota and Yukinori Yasui


The higher-dimensional Kerr–NUT–de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing–Yano (CKY) tensor as a ‘hidden’ symmetry which provides the separation of variables for the geodesic equations and Klein–Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr–NUT–de Sitter spacetime. In particular, we show that the Kerr–NUT–de Sitter spacetime is the only spacetime with a non-degenerate CKY tensor.

Closed conformal Killing–Yano tensor and the uniqueness of generalized Kerr–NUT– de Sitter spacetime

Philipp A Höhn and Susan M Scott


Quiescent cosmology and the Weyl curvature hypothesis possess a mathematical framework, namely the definition of an isotropic singularity, but only for the initial state of the universe. A complementary framework is necessary to also encode appropriate cosmological futures. In order to devise a new framework we analyse the relation between regular conformal structures and (an)isotropy, the behaviour and role of a monotonic

Encoding cosmological futures with conformal structures

conformal factor which is a function of cosmic time, as well as four example cosmologies for further guidance. Finally, we present our new definitions of an anisotropic future endless universe and an anisotropic future singularity which offer a promising realization for the new framework. Their irregular, degenerate conformal structures differ significantly from those of the isotropic singularity. The combination of the three definitions together could then provide the first complete formalization of the quiescent cosmology concept. For completeness we also present the new definitions of an isotropic future singularity and a future isotropic universe. The relation to other approaches, in particular to the somewhat dual dynamical systems approach, and other asymptotic scenarios is briefly discussed.

Ralf Aurich, Holger S Janzer, Sven Lustig and Frank Steiner


We compute the effects of a compact flat universe on the angular correlation function, the angular power spectrum, the circles-in-the-sky signature, and the covariance matrix of the spherical harmonics coefficients of the cosmic microwave background radiation using the full Boltzmann physics. Our analysis shows that the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data are compatible with the possibility that we live in a flat 3-torus with volume ∼− 5 × 103 Gpc3.

Do we live in a ‘small universe’?

Laura Mersini–Houghton and Fred C Adams


This paper investigates anthropic bounds on the vacuum energy Λ by considering alternate starting assumptions. We first consider the possibility of cosmic observers existing at any random time (including the future) for constant Λ, and take into account the suppression of new structure formation as the universe approaches its eternal de Sitter (DS) geometry. Structures that collapse prior to the era of Λ-domination will lose causal contact with our Hubble volume within a finite (short) conformal time τ∗. Any remnants within our Hubble volume then suffer a cosmological heat death after the universe becomes DS. The probability for finding observers by random measurements in the volume bound by the de Sitter horizon is proportional to the rate of change in the ratio of the 3-volume V

3(τ) to the 4-volume V

4(τ), so that P ∼− 0. This vanishing probability of populated DS volumes is a simple consequence of the information loss problem for eternal DS spaces resulting from the finite and constant value of its temperature TDS ∼− Λ−½ and entropy S = 3/(GΛ). By contrast, for geometries with Λ = 0, structures can condense and entropy production can continue without bounds at any epoch. The probability of finding observers in Λ = 0 geometries is thus overwhelming higher than in DS spaces. As a result, anthropic reasoning does not explain the small but nonzero vacuum energy observed in our universe. We also address the case where observers are considered only at a specially chosen time—like the present epoch—but relax the allowed values of starting density fluctuations and hence the redshift of galaxy formation. In this latter case, the bounds on a Λ can be millions of times larger than previous estimates—and the observed value. We thus conclude that anthropic reasoning has limited predictive power.

Limitations of anthropic predictions for the cosmological constant Λ: cosmic heat death of anthropic observers

Figure 2. The figure on the left shows (u, v)2, the square of the commutative wavefunction.







14 H i g h l i g h t s 2 0 0 9

Thomas Buchert and Mauro Carfora


We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question of whether it is sensible to assume that curvature averages out on some scale of homogeneity, as implied by the standard concordance model of cosmology, or whether the averaged scalar curvature can be largely negative today, as required for an explanation of dark energy from inhomogeneities. We confront both conjectures with a detailed analysis of the kinematical backreaction term and estimate its strength for a multi-scale inhomogeneous matter and curvature distribution. Our main result is a formula for the spatially averaged scalar curvature involving quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We propose strategies to quantitatively evaluate the formula, and pinpoint the assumptions implied by the conjecture of a small or zero averaged curvature. We reach the conclusion that the standard concordance model needs fine tuning in the sense of an assumed equipartition law for curvature in order to reconcile it with the estimated properties of the averaged physical space, whereas a negative averaged curvature is favoured, independent of the prior on the value of the cosmological constant.

On the curvature of the present-day universe

S Hild et al


All first-generation large-scale gravitational wave detectors are operated at the dark fringe and use a heterodyne readout employing radio frequency (RF) modulation–demodulation techniques. However, the experience in the currently running interferometers reveals several problems connected with a heterodyne readout, of which phase noise of the RF modulation is the most serious one. A homodyne detection scheme (DC-readout), using the highly stabilized and filtered carrier light as a local oscillator for the readout, is considered to be a favourable alternative. Recently a DC-readout scheme has been implemented on the GEO 600 detector. We describe the results of first measurements and give a comparison of the performance achieved with homodyne and heterodyne readout. The implications of the combined use of DC-readout and signal recycling are considered.

C-readout of a signal-recycled gravitational wave detector

B Abbott et al (for the LIGO Scientific Collaboration)


We present the results of the first joint search for gravitational-wave bursts by the LIGO and GEO 600 detectors. We search for bursts with characteristic central frequencies in the band 768–2048 Hz in the data acquired between 22 February and 23 March, 2005 (fourth LSC Science Run–S4). We discuss the inclusion of the GEO 600 data in the Waveburst–CorrPower pipeline that first searches for coincident excess power events without taking into account differences in the antenna responses or strain sensitivities of the various detectors. We compare the performance of this pipeline to that of the coherent Waveburst pipeline based on the maximum likelihood statistic. This likelihood statistic is derived from a coherent sum of the detector data streams that takes into account the antenna patterns and sensitivities of the different detectors in the network. We find that the coherent Waveburst pipeline is sensitive to signals of amplitude 30–50% smaller than the Waveburst–CorrPower pipeline. We perform a search for gravitational-wave bursts using both pipelines and find no detection candidates in the S4 data set when all four instruments were operating stably.

First joint search for gravitational-wave bursts in LIGO and GEO 600 data

Fumiko Kawazoe et al


Some next-generation gravitational-wave detectors, such as the American Advanced LIGO project and the Japanese LCGT project, plan to use power recycled resonant sideband extraction (RSE) interferometers for their interferometer’s optical configuration. A power recycled zero-detuning (PRZD) RSE interferometer, which is the default design for LCGT, has five main length degrees of freedom that need to be controlled in order to operate a gravitational-wave detector. This task is expected to be very challenging because of the complexity of optical configuration. A new control scheme for a PRZD RSE interferometer has been developed and tested with a prototype interferometer. The PRZD RSE interferometer was successfully locked with the control scheme. It is the first experimental demonstration of a PRZD RSE interferometer with suspended test masses. The result serves as an important step for the operation of LCGT.

Experimental investigation of a control scheme for a zero-detuning resonant sideband extraction interferometer for next-generation gravitational-wave detectors

Figure 4. l error

signal with SEM free and l

in lock.

Experimental gravity highlightsq

Figure 12. A pictorial representation of the (longitudinal) shear generated on a small sphere by three (independent) eigenvectors (i) i1,2,3, associated with the first (degenerate) eigenvalue

1 of the vector Laplacian ∆a

h. Such eigenvectors define a moving frame in which the shear is, in a L2-average sense, minimized. The region of near homogeneity D can be defined as the largest region in (, g) where we can introduce such minimal shear eigenvectors.






H i g h l i g h t s 2 0 0 9 15

F Acernese et al


In the framework of the expected association between gamma-ray bursts and gravitational waves, we present results of an analysis aimed to search for a burst of gravitational waves in coincidence with gamma-ray burst 050915a. This was a long duration gamma-ray burst detected by Swift during September 2005, when the Virgo gravitational wave detector was engaged in a commissioning run during which the best sensitivity attained in 2005 was exhibited. This offered the opportunity for Virgo’s first search for a gravitational wave signal in coincidence with a gamma-ray burst. The result of our study is a set of strain amplitude upper limits, based on the loudest event approach, for different but quite general types of burst signal waveforms. The best upper limit strain amplitudes we obtain are hrss = O(10–20) Hz−1/2 around ~200–1500 Hz. These upper limits allow us to evaluate the level up to which Virgo, when reaching nominal sensitivity, will be able to constrain the gravitational wave output associated with a long burst. Moreover, the analysis presented here plays the role of a prototype, crucial in defining a methodology for gamma-ray burst triggered searches with Virgo and opening the way for future joint analyses with LIGO.

Search for gravitational waves associated with GRB 050915a using the Virgo detector

C A van Eysden and A Melatos


The nonaxisymmetric Ekman flow excited inside a neutron star following a rotational glitch is calculated analytically including stratification and compressibility. For the largest glitches, the gravitational wave strain produced by the hydrodynamic mass quadrupole moment approaches the sensitivity range of advanced long-baseline interferometers. It is shown that the viscosity, compressibility and orientation of the star can be inferred in principle from the width and amplitude ratios of the Fourier peaks (at the spin frequency and its first harmonic) observed in the gravitational wave spectrum in the + and × polarizations. These transport coefficients constrain the equation of state of bulk nuclear matter, because they depend sensitively on the degree of superfluidity.

Gravitational radiation from pulsar glitches

J Mark Heinzle and Claes Uggla


We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. Surprisingly few facts are known about the ‘Mixmaster’ dynamics of these models, while at the same time most of the commonly held beliefs are rather vague. In this paper, we use Mixmaster facts as a base to build an infrastructure that makes it possible to sharpen the main Mixmaster beliefs. We formulate explicit conjectures concerning (i) the past asymptotic states of type IX solutions and (ii) the relevance of the Mixmaster/Kasner map for generic past asymptotic dynamics. The evidence for the conjectures is based on a study of the stochastic properties of this map in conjunction with dynamical systems techniques. We use a dynamical systems formulation, since this approach has so far been the only successful path to obtain theorems, but we also make comparisons with the ‘metric’ and Hamiltonian ‘billiard’ approaches.

Mixmaster: fact and belief

Vincent Moncrief and Oliver Rinne


When Einstein’s equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal factor and thus appear to be ill-behaved at this (exterior) boundary. In this paper however we show, through an enforcement of the Hamiltonian and momentum constraints to the needed order in a Taylor expansion, that these apparently singular terms are not only regular at the boundary but can in fact be explicitly evaluated there in terms of conformally regular geometric data. Though we employ a rather rigidly constrained and gauge-fixed formulation of the field equations, we discuss the extent to which we expect our results to have a more ‘universal’ significance and, in particular, to be applicable, after minor modifications, to alternative formulations.

Regularity of the Einstein equations at future null infinity

Figure 6. Width and amplitudes for the gravitational wave spectrum seen by a polar observershowing the effect of buoyancy and stratification.

Figure 6. Concatenating type II transition orbits we obtain sequences of transitions—heteroclinicchains. The discrete map governing the associated sequence of fixed points on K is the Mixmaster map. The arrows indicate the direction of time toward the past.

mathematical general relativity highlightsq






16 H i g h l i g h t s 2 0 0 9

Samuel E Gralla and Robert M Wald


There is general agreement that the MiSaTaQuWa equations should describe the motion of a ‘small body’ in general relativity, taking into account the leading order self-force effects. However, previous derivations of these equations have made a number of ad hoc assumptions and/or contain a number of unsatisfactory features. For example, all previous derivations have invoked, without proper justification, the step of ‘Lorenz gauge relaxation’, wherein the linearized Einstein equation is written in the form appropriate to the Lorenz gauge, but the Lorenz gauge condition is then not imposed—thereby making the resulting equations for the metric perturbation inequivalent to the linearized Einstein equations. (Such a ‘relaxation’ of the linearized Einstein equations is essential in order to avoid the conclusion that ‘point particles’ move on geodesics.) In this paper, we analyze the issue of ‘particle motion’ in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics, g

ab(λ), corresponding to having a body (or black hole) that is ‘scaled down’ to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric, gab(λ = 0). Gravitational self-force—as well as the force due to coupling of the spin of the body to curvature—then arises as a first-order perturbative correction in λ to this worldline. No assumptions are made in our analysis apart from the smoothness and limit properties of the one-parameter family of metrics, gab(λ). Our approach should provide a framework for systematically calculating higher order corrections to gravitational self-force, including higher multipole effects, although we do not attempt to go beyond first-order calculations here. The status of the MiSaTaQuWa equations is explained.

A rigorous derivation of gravitational self-force

Oliver Rinne


This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such schemes that have been proposed in the literature and show that some of their elliptic equations are indefinite, thus potentially admitting nonunique solutions and causing numerical solvers based on classical relaxation methods to fail. A new scheme is then presented that does not suffer from these problems. We use our numerical implementation to study the gravitational collapse of Brill waves. A highly prolate wave is shown to form a black hole rather than a naked singularity.

Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves

Luc Blanchet, Guillaume Faye, Bala R Iyer and Siddhartha Sinha


The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

Vincent Moncrief and James Isenberg


We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension n ≥ 4 contains a non-degenerate horizon with compact cross-sections that are transverse to the stationarity generating Killing vector field then, for each connected component of the black hole’s horizon, there is a Killing field which is tangent to the generators of the horizon. For the case of rotating black holes, the stationarity generating Killing field is not tangent to the horizon generators and therefore the isometry group of the spacetime is at least two dimensional. Our proof relies on significant extensions of our earlier work on the symmetries of spacetimes containing a compact Cauchy horizon, allowing now for non-closed generators of the horizon.

Symmetries of higher dimensional black holes

Black holes highlightsq

Numerical relativity highlightsq

DID YoU KNoW?...if you have source code relating to your computational work, you can now publish that code for free in CQG’s Published Software Archive? Published codes will remain freely available for perpetuity. See the CQG website for more details iopscience.org/cqg.Luis Lehner, Classical and Quantum Gravity Editorial Board Member






H i g h l i g h t s 2 0 0 9 17

David Kastor, Sourya Ray and Jennie Traschen


A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr relations and the mass and tension first laws for spacetimes containing both black holes and Killing bubbles. The resulting relations display an interesting interchange symmetry between the properties of black hole horizons and those of KK bubbles. This interchange symmetry reflects the underlying relation between static bubbles and black holes under double analytic continuation of the time and Kaluza–Klein directions. The thermodynamics of bubbles involve a geometrical quantity that we call the bubble surface gravity, which we show has several properties in common with the black hole surface gravity.

The thermodynamics of Kaluza–Klein black hole/bubble chains

Hari K Kunduri and James Lucietti


We consider stationary extremal black hole solutions of the Einstein–Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries and all static near-horizon geometries for black holes of this kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS

4 rotating extremal black hole is the near-horizon limit of extremal Kerr–Newman–AdS

4. We also identify the subset of near-horizon geometries which are supersymmetric. Finally, we show which physical quantities of extremal black holes may be computed from the near-horizon limit alone, and point out a simple formula for the entropy of the known supersymmetric AdS

4 black hole. Analogous results are presented in the case of a vanishing cosmological constant.

Uniqueness of near-horizon geometries of rotating extremal AdS4 black holes

Ran Li, Ji-Rong Ren and Shao-Wen Wei


We investigated Dirac particles’ Hawking radiation from the event horizon of the Kerr black hole in terms of the tunneling formalism. Applying the WKB approximation to the general covariant Dirac equation in the Kerr spacetime background, we obtain the tunneling probability for fermions and Hawking temperature of the Kerr black hole. The result obtained by taking the fermion tunneling into account is consistent with the previous literature.

Hawking radiation of Dirac particles via tunneling from the Kerr black hole

Parampreet Singh


A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model-independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective loop quantum spacetime. Further, if the evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exists a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives will always diverge. Such events however turn out to be harmless weak curvature singularities beyond which geodesics can be extended. Our results point toward a generic resolution of physical singularities in LQC.

Are loop quantum cosmos never singular?

Ali Kaya


In the context of quantum fields in time-dependent classical backgrounds, we note that the number of created particles with a given momentum largely deviates about its mean value. Guided with this observation we use a complete orthonormal family of localized wave packets to calculate the deviations in the number and energy densities of particles produced in a volume of a given size during reheating. It turns out that at the end of reheating there exist (in general tiny) spatial variations in these densities on Hubble length scales over which local interactions are incapable of restoring homogeneity. This signals the destruction of perfect homogeneity attained after inflation due to the quantum nature of the particle production process in reheating.

Quantum-mechanical breakdown of perfect homogeneity in reheating after inflation

Ding Wang, R B Zhang and Xiao Zhang


A quantum Schwarzschild spacetime and a quantum Schwarzschild–de Sitter spacetime with a cosmological constant Λ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The metrics and curvatures of the quantum Schwarzschild spacetime and the quantum Schwarzschild–de Sitter spacetime are computed. It is shown that up to the second order in the deformation parameter, the quantum spacetimes are solutions of a noncommutative Einstein equation.

Quantum deformations of Schwarzschild and Schwarzschild–de Sitter spacetimes

Quantum cosmology highlightsq








18 H i g h l i g h t s 2 0 0 9

Madhavan Varadarajan


In contrast to previous work in the field, we construct the loop quantum cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the Hamiltonian constraint. The matter part of the constraint contains the inverse triad operator which can be quantized with or without the use of a Thiemann-like procedure. With the latter choice, we show that the LQC quantization is identical to that of the standard Wheeler–DeWitt theory (WDW) wherein there is no singularity resolution. We argue that the former choice leads to singularity resolution in the sense of a well-defined, regular (backward) evolution through and beyond the epoch where the size of the universe vanishes. Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three ‘exotic’ structures in this LQC model, namely: curvature corrections, inverse triad definitions and the ‘polymer’ nature of the kinematic representation. We also critically examine certain technical assumptions made by APS in their analysis of WDW semiclassical states and point out some problems stemming from the infrared behaviour of their wavefunctions.

On the resolution of the big bang singularity in isotropic loop quantum cosmology

Wojciech Kaminski, Jerzy Lewandowski and Tomasz Pawłowski


Several conceptual aspects of quantum gravity (QG) are studied on the example of the homogeneous isotropic loop quantum cosmology (LQC) model. In particular: (i) the proper time of the comoving observers is shown to be a quantum operator and a quantum spacetime metric tensor operator is derived. (ii) Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. In particular it is shown that in the case of a model with massless scalar field and cosmological constant Λ, the physical Hilbert spaces constructed for two choices of lapse are the same for Λ < 0 while they are significantly different for Λ > 0. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator, whose essential spectrum was shown to be an interval [0, ρcr], where ρcr ≈ 0.41 ρPI. (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables.

Physical time and other conceptual issues of quantum gravity on the example of loop quantum cosmology

L A Forte


In this paper, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass automorphic forms and recent mathematical results about arithmetical dynamical systems. The predictions of the billiard model give precise automorphic properties for the wavefunction (Maass–Hecke eigenform), the asymptotic number of quantum states (Selberg asymptotics for PSL (2, Ζ), the distribution for the level spacing statistics (the Poissonian one) and the absence of scarred states. The most interesting implication of this model is perhaps that the discrete spectrum is fully embedded in the continuous one.

Arithmetical chaos and quantum cosmology

Claus Gerhardt


We consider the Wheeler–DeWitt equation Hψ = 0 in a suitable Hilbert space. It turns out that this equation has countably many solutions ψ, which can be considered as eigenfunctions of a Hamilton operator implicitly defined by H. We consider two models, a bounded one, 0 < r < r

0, and an unbounded, 0 < r < ∞, which represent different eigenvalue problems. In the bounded model we look for eigenvalues Λi, where the Λi are the values of the cosmological constant which we used in the Einstein–Hilbert functional, and in the unbounded model the eigenvalues are given by

where Λi < 0. Note that r is the symbol for the scale factor, usually denoted by a, or a power of it. The ψ form a basis of the underlying Hilbert space. We prove furthermore that the implicitly defined Hamilton operator is selfadjoint and that the solutions of the corresponding Schrödinger equation satisfy the Wheeler–DeWitt equation, if the initial values are superpositions of eigenstates. All solutions have an initial singularity in r = 0. Under certain circumstances a smooth transition from big crunch to big bang is possible.

Quantum cosmological Friedman models with an initial singularity

K( ) nn 1

i− − −

Look out for the special CQG Cluster Issue on Non-linear Cosmological Perturbations to be published in the Summer of 2010.

This cluster issue is not based on any conference, but is instead a collection of specially chosen high-quality articles in a rapidly developing sub-field of Cosmology. Articles in this special issue will be made free to download for 6 months from their date of online publication.

David Wands and Misao Sasaki, Editors of the Nonlinear Cosmological Perturbations Cluster issue






H i g h l i g h t s 2 0 0 9 19

Ghanashyam Date and Sandipan Sengupta


Quantum corrections of certain types and relevant in certain regimes can be summarized in terms of an effective action calculable, in principle, from the underlying theory. The demands of symmetries, local form of terms and dimensional considerations limit the form of the effective action to a great extent leaving only the numerical coefficients to distinguish different underlying theories. The effective action can be restricted to particular symmetry sectors to obtain the corresponding, reduced effective action. Alternatively, one can also quantize a classically (symmetry) reduced theory and obtain the corresponding effective action. These two effective actions can be compared. As an example, we compare the effective action(s) known in isotropic loop quantum cosmology with the Lovelock actions, as well as with more general actions, specialized to homogeneous isotropic spacetimes and find that the m -scheme is singled out.

Effective actions from loop quantum cosmology: correspondence with higher curvature gravity

N C Tsamis and R P Woodard


Inflationary quantum gravity simplifies drastically in the leading logarithm approximation. We show that the only counterterm which contributes in this limit is the 1-loop renormalization of the cosmological constant. We go further to make a simplifying assumption about the operator dynamics at leading logarithm order. This assumption is explicitly implemented at 1- and 2-loop orders, and we describe how it can be implemented nonperturbatively. We also compute the expectation value of an invariant observable designed to quantify the quantum gravitational back-reaction on inflation. Although our dynamical assumption may not prove to be completely correct, it does have the right time dependence, it can naturally produce primordial perturbations of the right strength, and it illustrates how a rigorous application of the leading logarithm approximation might work in quantum gravity. It also serves as a partial test of the ‘null hypothesis’ that there are no significant effects from infrared gravitons.

A simplified quantum gravitational model of inflation

Martin Bojowald


A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an isotropic universe filled with a free, massless scalar field would bounce must be well below the Planck density. In the presence of anisotropy, no model of the Schwarzschild black hole interior analyzed so far is consistent.

Consistent loop quantum cosmology

Daniele Colosi and Carlo Rovelli


Theoretical developments related to gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely defined particle states do not exist in general, in QFT on a curved spacetime. More generally, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have led some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or ‘particle’ physics. Here we offer an element of clarification by observing that already in flat space there exist—strictly speaking—two distinct notions of particles: globally defined n-particle Fock-states and local particle states. The last describes the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories—it amounts to a reminder that there are boundary effects in realistic detectors—but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of the local particle state that remains well defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity.

What is a particle?

Florian Conrady and Laurent Freidel


We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov’s and Livine’s SO(4) projected states. For 0 γ 1, the states can be restricted to SU(2) spin networks.

Path integral representation of spin foam models of 4D gravity

Figure 1. (a) Face f of dual complex ∆*. (b) Subdivision of face f into wedges. The arrowsindicate starting point and orientation for wedge holonomies.

Quantum gravity highlightsq







20 H i g h l i g h t s 2 0 0 9

Aaron J Amsel and Donald Marolf


Boundary conditions for massive fermions are investigated in AdSd for d ≥ 2. For fermion masses in the range 0 ≤ |m| < 1/2l with l being the AdS length, the standard notion of normalizeability allows a choice of boundary conditions. As in the case of scalars at or slightly above the Breitenlohner–Freedman (BF) bound, such boundary conditions correspond to multi-trace deformations of any CFT dual. By constructing appropriate boundary superfields, for d = 3, 4, 5 we identify joint scalar/fermion boundary conditions which preserve either N = 1 supersymmetry or N = 1 superconformal symmetry on the boundary. In particular, we identify boundary conditions corresponding via AdS/CFT (at large N) to a 595-parameter family of double-trace marginal deformations of the low-energy theory of N M2-branes which preserve N = 1 superconformal symmetry. We also establish that (at large N and large ‘t Hooft coupling λ) there are no marginal or relevant multi-trace deformations of 3+1 N = 4 super Yang–Mills which preserve even N = 1 supersymmetry.

Supersymmetric multi-trace boundary conditions in AdS

Changhyun Ahn


Four-dimensional field equations are determined for perturbations of the quotient 7-sphere size and squashing parameter in 11-dimensional supergravity. The quotient 7-sphere is an S1-bundle over the CP3 which is regarded as an S2-fibration over the base S4. By analyzing the AdS4 supergravity scalar potential, the holographic supersymmetric (or nonsupersymmetric) renormalization group (RG) flow from N = 1 (or N = 0) SO(5) × U(1)-invariant UV fixed point to N = 6 (or N = 0) SU(4)R × U(1)-invariant IR fixed point is obtained. The three-dimensional boundary theories are described by superconformal Chern–Simons matter theories and a dual operator corresponding to this RG flow is described.

Squashing gravity dual of N = 6 superconformal Chern–Simons gauge theory

Igor A Bandos and Paul K Townsend


We present the light-cone gauge fixed Lagrangian for the M5-brane; it has a residual ‘exotic’ gauge invariance with the group of 5-volume preserving diffeomorphisms, SDiff5, as gauge group. For an M5-brane of topology R2 × M3, for closed 3-manifold M3, we find an infinite tension limit that yields an SO(8)-invariant (1 + 2)-dimensional field theory with ‘exotic’ SDiff

3 gauge invariance. We show that this field theory is the Carrollian limit of the Nambu bracket realization of the ‘BLG’ model for multiple M2-branes.

Light-cone M5 and multiple M2-branes

Przemysław Małkiewicz and Włodzimierz Piechocki


We present analytical results on the propagation of a classical string in nonzero modes through the singularity of the compactified Milne space. We restrict our analysis to a string winding around the compact dimension of spacetime. The compact dimension undergoes contraction to a point followed by re-expansion. We demonstrate that the classical dynamics of the string in excited states is non-singular in the entire spacetime.

Excited states of a string in a time-dependent orbifold

A Pravdová and V Pravda


Vacuum spacetimes admitting a non-twisting geodetic multiple Weyl aligned null direction (WAND) are analysed in arbitrary dimension using a recently developed higher-dimensional Newman–Penrose (NP) formalism. We determine the dependence of the metric and of the Weyl tensor on the affine parameter r along null geodesics generated by the WAND for type III and N spacetimes and for a special class of type II and D spacetimes, containing e.g. Schwarzschild–Tangherlini black holes and black strings and branes. For types III and N, all metric components are at most quadratic polynomials in r while for types II and D the r-dependence of the metric as well as of the Weyl tensor is determined by an integer m corresponding to the rank of the expansion matrix Sij. It is shown that for non-vanishing expansion, all these spacetimes contain a curvature singularity. As an illustrative example, a shearing expanding type N five-dimensional vacuum solution is also re-derived using higher-dimensional NP formalism. This solution can be, however, identified with a direct product of a known four-dimensional type N metric with an extra dimension.

The Newman–Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction

Figure 1. Compactified 2D Milne space embedded in 3D Minkowski space.

Strings, branes, supergravity and gauge theory highlights

q

DID YoU KNoW?CQG is one of the most selective journals in the field?

CQG accepted 40.7% of regular submissions to the journal in 2009, ensuring that only internationally competitive papers

of a very high quality are to be found in CQG.







H i g h l i g h t s 2 0 0 9 21

José Figueroa-O’Farrill, Emily Hackett-Jones, George Moutsopoulos and Joan Simón


In this paper we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund–Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund–Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS

4 × S7 and find that it is isomorphic to osp(132). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS

4 × S7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement.

On the maximal superalgebras of supersymmetric backgrounds

G S Hall and D P Lonie


There has been some recent interest in the relation between two spacetimes which have the same geodesic paths, that is, spacetimes which are projectively equivalent (sometimes called geodesically equivalent). This paper presents a short and accessible proof of the theorem that if two spacetimes have the same geodesic paths and one of them is an Einstein space then (either each is of constant curvature or) their Lévi-Civitá connections are identical. It also clarifies the relationship between their associated metrics. The results are extended to include the signatures (+ + + +) and (− − + +), and some examples and discussion are given in the case of dimension n > 4. Some remarks are also made which show how these results may be useful in the study of projective symmetry.

Projective equivalence of Einstein spaces in general relativity

Robert Beig and Richard M Schoen


The static n-body problem of general relativity states that there are, under a reasonable energy condition, no static n-body configurations for n > 1, provided the configuration of the bodies satisfies a suitable separation condition. In this paper we solve this problem in the case that there exists a closed, noncompact, totally geodesic surface disjoint from the bodies. This covers the situation where the configuration has a reflection symmetry across a noncompact surface disjoint from the bodies.

On static n-body configurations in relativity

Kory A Stevens, Kristin Schleich and Donald M Witt


Geons, small topological structures that exhibit particle properties such as charge and angular momentum without the presence of matter sources, have been extensively discussed in (3 + 1)-dimensional general relativity. Given the recent renewal of interest in (2 + 1) gravity, it is natural to ask whether or not the notion of geons extends to three dimensions. We prove here that, in contrast to the (3 + 1)-dimensional case, there are no (2 + 1)-dimensional asymptotically flat solutions of the vacuum Einstein or Einstein–Maxwell equations containing geons. In contrast, (2 + 1)-dimensional asymptotically anti-de Sitter spacetimes can indeed contain geons; however, the geons are always hidden behind a single black hole horizon. We also prove sufficient conditions for the non-existence of (2 + 1)-dimensional asymptotically flat geon-containing solutions.

Non-existence of asymptotically flat geons in (2 + 1) gravity

Abraham I Harte


A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincaré and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.

Approximate spacetime symmetries and conservation laws

Geometry and topology highlightsq

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22 H i g h l i g h t s 2 0 0 9

Richard J Epp, Robert B Mann and Paul L McGrath


In this first of a series of papers we will introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a ‘system’ in the context of the dynamical spacetime of general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary (topologically R × S2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (the ‘size’ of the system is not changing) and shear-free (the ‘shape’ of the system is not changing). This definition of a system is anticipated to yield simple, exact geometrical insights into the problem of motion in general relativity. It begins by answering, in a precise way, the questions of what is in motion (a rigid two-dimensional system boundary with topology S2, and whatever matter and/or radiation it happens to contain at the moment), and what motions of this rigid boundary are possible. Nearly a century ago Herglotz and Noether showed that a three-parameter family of timelike worldlines in Minkowski space satisfying Born’s 1909 rigidity conditions does not have the 6 degrees of freedom we are familiar with from Newtonian mechanics, but a smaller number—essentially only 3. This result curtailed, to a large extent, subsequent study of rigid motion in special and (later) general relativity. We will argue that in fact we can implement Born’s notion of rigid motion in both flat spacetime (this paper) and arbitrary curved spacetimes containing sources (subsequent

papers)—with precisely the expected 3 translational and 3 rotational degrees of freedom (with arbitrary time dependence)—provided the system is defined quasilocally as the two-dimensional set of points comprising the boundary of a finite spatial volume, rather than the three-dimensional set of points within the volume.

Rigid motion revisited: rigid quasilocal frames

G W Gibbons and M C Werner


In this geometrical approach to gravitational lensing theory, we apply the Gauss–Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.

Applications of the Gauss–Bonnet theorem to gravitational lensing

Do-Hyung Kim


It is shown that if a spacetime has a non-compact Cauchy surface Σ, then its causal structure is completely determined by the class of compact subsets of Σ of the forms J−(p)∩Σ and J+(p)∩Σ. Since the causal structure determines its metric structure up to a conformal factor, this implies that the sets J−(p)∩Σ and J+(p)∩Σ determine the conformal structure of a globally hyperbolic spacetime. In this way, we can encode the conformal structure of the spacetime into its Cauchy surface and we get another method for reconstructing spacetime.

A note on non-compact Cauchy surfaces

Marcus A Khuri


We establish a positive mass theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular, we answer a question posed by R Wald concerning the existence of generalized apparent horizons in Minkowski space.

A note on the nonexistence of generalized apparent horizons in Minkowski space

Figure 1. The shape of the rotating observers’ round sphere as seen by observers in the inertial reference frame: plots of the parametric curve P (), Z z() for r 1 and 0, 1 and 5. The last case corresponds to v

equator 0.98c. The dots show the locations of observers with 0, /6, 2/6, . . . , . Since there is no length contraction in a constant plane, the dots are equally spaced along each curve.

Figure 1. Weak deflection lensing geometry. Two geodesics 1 and 2 from the source S to theobserver O are deflected by a lens with centre at L. D

1 and D2 are two domains with boundary curves L and D as discussed in the text.

comments, Replies and Notes highlightsq

cQG Impact FactoRSCQG has seen a consistent rise in Impact Factor.

The most recent (2008) measurement shows the journal at an all-time high.

2006 2007 2008

2.773* 2.846* 3.035** As listed in ISI®’s 2006, 2007 and 2008 Science Citation Index Journal citation reports





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