Astrophysical tests of general relativity in the

strong-field regime

Emanuele Berti, University of Mississippi/CaltechTexas Symposium, São Paulo, Dec 18 2012

1) What are “strong field” tests?2) Alternatives to GR: massive

scalars3) BH dynamics and

superradiance4) GWs: SNR and event rates

(e)LISA and fundamental physics

5) BH spins and photon mass bounds

Coda: Advanced LIGO and astrophysics

Strong field: gravitational field vs. curvature; probing vs. testing

[Psaltis, Living Reviews in Relativity]

Testing general relativity – against what?

Finding a contender Action principle Well-posed initial-value problem At most second-order equations of motion Testable predictions!

Dynamical Chern-SimonsEinstein-dilaton-Gauss-Bonnet

Generic scalar-tensor theory

[Clifton+, 1106.2476]

A promising opponent: massive scalar fields

1) Phenomenology Modern equivalent of planets [Bertschinger] Well-posed, flexible (Damour & Esposito-Farése “spontaneous scalarization”) f(R) and other theories equivalent to scalar-tensor theories

2) High-energy physics Standard Model extensions predict massive scalar fields (dilaton, axions, moduli…) Not seen yet: dynamics must be frozen

small coupling x - or equivalently large wBD~1/x large mass m>1/R (1AU~10-18eV!)

3) Cosmology “String axiverse”: light axions, 10-33eV < ms < 10-18eV [Arvanitaki++, 0905.4720]

Striking astrophysical implications: bosenovas, floating orbits

Are massive scalar fields viable?Bounds from:

Shapiro time delay: wBD>40,000 [Perivolaropoulos, 0911.3401] Lunar Laser Ranging Binary pulsars: wBD>25,000 [Freire++, 1205.1450]

[Alsing, EB, Will & Zaglauer, 1112.4903]

Wave scattering in rotating black holes

Quasinormal modes: Ingoing waves at the horizon,

outgoing waves at infinity Discrete spectrum of damped

exponentials (“ringdown”)[EB++, 0905.2975]

Massive scalar field:

Superradiance: black hole bomb when 0 < w < mWH

Hydrogen-like, unstable bound states [Detweiler, Zouros+Eardley…]

[Arvanitaki+Dubovsky, 1004.3558]

f = 1.2 x 10-2 (106Msun)/M Hzt = 55 M/(106Msun) s

In GR, each mode determined uniquely by mass and spin

One mode: (M,a)Any other mode frequency:No-hair theorem test

Relative mode amplitudes:pre-merger parameters[Kamaretsos++,Gossan++]

Feasibility depends on SNR:Need SNR>30 [EB++, 2005/07]

1) Noise S(fQNM)2) Signal h~E1/2, E=erdM

erd~0.01(4h)2 for comparable-mass mergers, h=m1m2/(m1+m2)2

Quasinormal modes[Visualization: NASA Goddard]

(e)LISA vs. LIGO

[Schutz; see Sesana’s talk]

SNR=h/S: S comparable, h~hM1/2

f = 1.2 x 10-2 (106Msun)/M Hzt = 55 M/(106Msun) s

LISA/eLISA studies:merger-tree models of SMBH formation

Light or heavy seeds?Coherent or chaotic accretion?[Arun++, 0811.1011]

eLISA can easily tell whetherseeds are light or heavy[Sesana++, 1011.5893]

Mergers: a~0.7Chaotic accretion: a~0Coherent accretion: a~1[EB+Volonteri, 0802.0025]

>10 binaries can be used for no-hair tests Spin observations constrain SMBH formation

Ringdown as a probe of SMBH formation

[Sesana++, 2012]

Massive bosonic fields and superradiant instabilities

Superradiance when w < mWH

Any light scalar can trigger a black hole bomb (“bosenova”)[Yoshino+Kodama, 1203.5070]

Strongest instability: msM~1[Dolan, 0705.2880]

For ms=1eV, M=Msun : msM~1010

Need light scalars (or primordial black holes!)

Negative scalar flux at the horizon close to superradiant resonances at

[Detweiler 1980]

Light scalars: floating orbits (Press & Teukolsky 1972)

[Cardoso++ 1109.6021; Yunes++, 1112.3351]

Photon mass bound from rotating black holes

Proca perturbations in Kerrdo not decouple

Use Kojima’sslow-rotation approximation

Stronger instabilitythan for massive scalars

Maximum (again) for msM~1

mg<10-20 (or 4x10-21) eVPDG: mg<10-18 eV

[Pani++, 1209.0465; 1209.0773]

[Data points: Brenneman++, 1104.1132]

[Schnittman 04; Kesden++; Lousto’s talk]

Spin-orbit resonances and spin alignment

Can Advanced LIGO reconstruct binary evolution?[Gerosa++, in preparation]

Tests within GR1) (e)LISA: Tens of events could allow us to test the no-hair

theoremAdvanced LIGO/ET can also test no-hair theorem - if IMBHs exist!

2) Spin measurements constrain SMBH merger/accretion history

[EB++, 0905.2975; EB+Volonteri, 0802.0025]

Massive bosons and superradiant instabilities3) Weak-field: Solar System, binary pulsars

Cassini: wBD>40,000 for ms<2.5x10-20 eV Binary pulsars will do better in a few years

[Alsing++, 1112.4903; Horbatsch++, in preparation]4) Massive scalars: floating orbits

[Cardoso++, 1109.6021; Yunes++, 1112.3351]5) Massive vectors and SMBH spins: best bounds on photon mass

mg<10-20 (4x10-21eV) (Particle Data Group: mg<10-18eV) [Pani++, 1209.0465; 1209.0773]

Advanced LIGO6) Spin alignment may encode formation history of the binary

Effect of tides? Reverse mass ratio?

Summary