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Sven Köppel
The Generalized Uncertainty Principleand Extra Dimensions
Geometry and Physics seminarDFT at IFIN-HH, Bucharest
September 25, 2015
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Coworkers:
Marco KnipferPD Dr. Piero Nicolini
Maximiliano IsiProf. Jonas Mureika
Sven Köppel
The Generalized Uncertainty Principleand Extra Dimensions
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OutlineWhy do we need models for Quantum Black Holes?
Modifying Heisenberg's uncertainty principle
Features of a certain class of nonlocal gravity spacetimes
Extension to Large extra dimensions
Further extensions / comments about ...
… Analytic continuation to negative radii
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Motivation: Why minimal length physics?
Aurilia, Spallucci 2002Dvali, Gomez 2010Carr 2014
UV-Complete Gravity,Minimal length
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Motivation: Why minimal length physics?
Aurilia, Spallucci 2002Dvali, Gomez 2010Carr 2014
UV-Complete Gravity,Minimal length
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The Planck scale
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Motivation: Why minimal length physics?
Aurilia, Spallucci 2002Dvali, Gomez 2010Carr 2014
UV-Complete Gravity,Minimal length
Constrain physicallyallowed region
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The Planck scale
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Schwarzschild BHs exhibit problems
The Schwarzschild black hole is not suitable to describe „smallest distances“:
Curvature singularity ill defined thermodynamics
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Quantum black holes in nature?
Carr 2014Bleicher, Nicolini 2010, 2014
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Quantum black holes in nature?
Primordial black holes
Black Hole
Evaporate ~ „now“
Carr 2014Bleicher, Nicolini 2010, 2014
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Quantum black holes in nature?
Primordial black holes Particle accelerators
Black Hole
Immediately evaporatesEvaporate ~ „now“
10 TeV: Requires extra dimensions!
Carr 2014Bleicher, Nicolini 2010, 2014
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Black hole evaporation
Remnants: Candidates for cold dark matterHossenfelder 2004Hossenfelder LRR 2013
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Effective quantum gravity equations
Quantum matter
Nonlocal spacetime
dual theory
Nonlocal operatorInfluenced by one of:
String theoryLoop quantum gravityAsymptotically safe gravityNoncommutative geometry
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HeavisideStep function
Cumulatedmass
r
M
r
M
„Smeared“Mass
Cumulatedmass
DiracDelta function
Occuring inT_{00}
rr
„Smeared“Mass
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A quantum theory of gravity must be nonlocal
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The Generalized Uncertainty Principleas a guiding principle for the quantum corrections to GR
Veneziano 1986Amati, Veneziano, Ciafaloni 1995Michele Maggiore 1995Kempf, Mangano, Mann 1996
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The Generalized Uncertainty Principleas a guiding principle for the quantum corrections to GR
Veneziano 1986Amati, Veneziano, Ciafaloni 1995Michele Maggiore 1995Kempf, Mangano, Mann 1996
Physically allowed regionby GUP prediction
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GUP: Approximation to Temperature: Hot remnants
Adler, Santiago 1999Adler, Chen, Santiago 2001
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GUP: Approximation to Temperature: Hot remnants
Adler, Santiago 1999Adler, Chen, Santiago 2001
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GUP: Approximation to Temperature: Hot remnants
Hot evaporation endpoint
Hawking temperature
Adler, Santiago 1999Adler, Chen, Santiago 2001
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GUP: Exploiting a Hilbert space representation
Hilbert spacerepresentation
Kempf, Mangano, Mann 1996
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GUP: Exploiting a Hilbert space representation
Hilbert spacerepresentation
Kempf, Mangano, Mann 1996
Approximationin nonlocal Lagrangiangives nonlocal EFE
Krasnikov 1987,Modesto 2012, 2013Moffat 2012Choose
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GUP: Exploiting a Hilbert space representation
Isi, Mureika, Nicolini 2013Balazin, Nachbagauer 1994
What is the effect ona Schwarzschild BH?
Hilbert spacerepresentation
Kempf, Mangano, Mann 1996
Approximationin nonlocal Lagrangiangives nonlocal EFE
Krasnikov 1987,Modesto 2012, 2013Moffat 2012Choose
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GUP: Exploiting a Hilbert space representation
Isi, Mureika, Nicolini 2013Balazin, Nachbagauer 1994
What is the effect ona Schwarzschild BH?
Modified Newton'spotential
Hilbert spacerepresentation
Kempf, Mangano, Mann 1996
Approximationin nonlocal Lagrangiangives nonlocal EFE
Krasnikov 1987,Modesto 2012, 2013Moffat 2012Choose
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GUP: Exploiting a Hilbert space representation
Isi, Mureika, Nicolini 2013Balazin, Nachbagauer 1994
What is the effect ona Schwarzschild BH?
Modified Newton'spotential
Analytical result:
Hilbert spacerepresentation
Kempf, Mangano, Mann 1996
Approximationin nonlocal Lagrangiangives nonlocal EFE
Krasnikov 1987,Modesto 2012, 2013Moffat 2012Choose
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Isi, Mureika,Nicolini 2013
GUP inspired Black holes: Self completeness
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Isi, Mureika,Nicolini 2013
GUP inspired Black holes: Self completeness
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Isi, Mureika,Nicolini 2013
GUP inspired Black holes: Self completeness
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Isi, Mureika,Nicolini 2013
GUP inspired Black holes: Self completeness
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Isi, Mureika,Nicolini 2013
GUP inspired Black holes: Self completeness
Self complete: Can relate free parameter to fundamental length
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The black hole remnant: thermodynamics
semiclassical regimecooldownphase
inaccessibleregime
Temperature:
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The black hole remnant: thermodynamics
semiclassical regimecooldownphase
inaccessibleregime
Phase transitionHeatcapacity
Temperature:
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The black hole remnant: thermodynamics
semiclassical regimecooldownphase
inaccessibleregime
Phase transitionHeatcapacity
Temperature:
Entropy
The remnant:A cold stableevaporationendpoint
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Extension of such models
Alternative theories of gravity:Large extra dimensions+ Terascale physics+ Hawking emission on brane/bulk
or adding more complexity+ Angular momentum+ Electrical charge+ AdS background
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Adressing the weak hierarchy problem of the Standard Model
Elektroweak scalevs.
Planck scale
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Large Extra Dimensions
ADD scenario
Integrated huge Volume ofextra dimensions
Large µm up to mm
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Large Extra Dimensions
ADD scenario
Integrated huge Volume ofextra dimensions
Large µm up to mm
Arkani-HamedDimopoulosDvali 1998
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The Kempf-Mangano-Mann model in N+1 dimensions
Apply the momentum space regularization in N spatial dimensions (ADD model)
Kempf, Mangano, Mann 1996Scardigli, Casadio 2003
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The Kempf-Mangano-Mann model in N+1 dimensions
Apply the momentum space regularization in N spatial dimensions (ADD model)
Kempf, Mangano, Mann 1996Scardigli, Casadio 2003
We can solve the nonlocal operator analytically in any number of extradimensions
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One extra dimension
GUP-inspired BH in higher dimensions
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One extra dimension
GUP-inspired BH in higher dimensions
More than one extra dimension
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GUP-inspired BH in higher dimensions
No more remnants in higher (N > 4) dimensions.
One extra dimension More than one extra dimension
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Adler 2010Carr 2014
Retracing a popular Gedankenexperiment
The Heisenberg microscope in n LXDs:
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This Gedankenexperiment motivates a modified GUP:
Constant integrand: Sounds reasonable
We can solve this spacetime analytically in any dimension.
Adler 2010Carr 2014
Retracing a popular Gedankenexperiment
The Heisenberg microscope in n LXDs:
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Modified GUP inspired Black Holes
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Modified GUP inspired Black Holes
Gravitational potential with 4 extra dimensions:
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Modified GUP inspired Black Holes
Gravitational potential with 1 extra dimension:
Pathologies!
Gravitational potential with 4 extra dimensions:
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GUP in extra dimensions: Ways out
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Maziashvili 2013
GUP in extra dimensions: Ways out
• Improve GUP. Example:
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Maziashvili 2013
GUP in extra dimensions: Ways out
• Improve GUP. Example:
• Improve NLG. Include higher derivative terms in nonlocal operator
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Maziashvili 2013
GUP in extra dimensions: Ways out
• Improve GUP. Example:
• Improve NLG. Include higher derivative terms in nonlocal operator
• Propose nonsingular model.Model engineering
Hayward 2006
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Analytical continuation
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Analytical continuation
Schwarzschild BH
GUP-inspired BH
Finite curvature BH
Softening the Ricci curvature scalar divergence
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Analytical continuation
Schwarzschild BH
GUP-inspired BH
Finite curvature BH
Softening the Ricci curvature scalar divergence
Analytical continuation:
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Sven Köppel
The Generalized Uncertainty Principleand Extra Dimensions
Thank you for your attention!
References
Ongoing
Isi, Mureika, NicoliniSelf-Completeness and the GUP[JHEP 2013]
Köppel, Isi, Knipfer, Mureika, NicoliniSelf-Completeness and the GUPin extradimensions
Köppel, Knipfer, Dirkes, Frassino, Nicolini, BleicherGUP and BHs – a pedagogical review