1. The Generalized Uncertainty Principle and Extra Dimensions
Sven Köppel
The Generalized Uncertainty Principle
and Extra Dimensions
Geometry and Physics seminar
DFT at IFIN-HH, Bucharest
September 25, 2015

2. The Generalized Uncertainty Principle and Extra Dimensions
Sven Köppel
The Generalized Uncertainty Principle
and Extra Dimensions
Coworkers:
Marco Knipfer
PD Dr. Piero Nicolini
Maximiliano Isi
Prof. Jonas Mureika

3. Outline Why do we need models for Quantum Black Holes?
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Outline
Why 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

4. Motivation: Why minimal length physics?
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Motivation: Why minimal length physics?
Aurilia, Spallucci 2002
Dvali, Gomez 2010
Carr 2014
UV-Complete Gravity,
Minimal length

5. Motivation: Why minimal length physics?
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Motivation: Why minimal length physics?
Aurilia, Spallucci 2002
Dvali, Gomez 2010
Carr 2014
UV-Complete Gravity,
Minimal length
The Planck scale

6. Motivation: Why minimal length physics?
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Motivation: Why minimal length physics?
Constrain physically
allowed region
Aurilia, Spallucci 2002
Dvali, Gomez 2010
Carr 2014
UV-Complete Gravity,
Minimal length
The Planck scale

7. Schwarzschild BHs exhibit problems
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Schwarzschild BHs exhibit problems
The Schwarzschild black hole is not suitable to describe „smallest distances“:
Curvature singularity
ill defined thermodynamics

8. Quantum black holes in nature?
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Quantum black holes in nature?
Carr 2014
Bleicher, Nicolini 2010, 2014

9. Quantum black holes in nature?
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Quantum black holes in nature?
Primordial black holes
Black Hole
Evaporate ~ „now“
Carr 2014
Bleicher, Nicolini 2010, 2014

10. Quantum black holes in nature?
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Quantum black holes in nature?
Primordial black holes
Particle accelerators
Black Hole
Evaporate ~ „now“
Immediately evaporates
10 TeV: Requires extra dimensions!
Carr 2014
Bleicher, Nicolini 2010, 2014

11. Black hole evaporation
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Black hole evaporation
Remnants: Candidates for cold dark matter
Hossenfelder 2004
Hossenfelder LRR 2013

12. Effective quantum gravity equations
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Effective quantum gravity equations
Influenced by one of:
String theory
Loop quantum gravity
Asymptotically safe gravity
Noncommutative geometry
Nonlocal operator
Quantum matter
dual theory
Nonlocal spacetime

13. A quantum theory of gravity must be nonlocal
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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A quantum theory of gravity must be nonlocal M M
Heaviside
Step function
Cumulated
mass
„Smeared“
Mass
Cumulated
mass r r
Dirac
Delta function
Occuring in
T_{00}
„Smeared“
Mass r r

14. The Generalized Uncertainty Principle
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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The Generalized Uncertainty Principle
as a guiding principle for the quantum corrections to GR
Veneziano 1986
Amati, Veneziano, Ciafaloni 1995
Michele Maggiore 1995
Kempf, Mangano, Mann 1996

15. Physically allowed region
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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The Generalized Uncertainty Principle
as a guiding principle for the quantum corrections to GR
Veneziano 1986
Amati, Veneziano, Ciafaloni 1995
Michele Maggiore 1995
Kempf, Mangano, Mann 1996
Physically allowed region
by GUP prediction

16. GUP: Approximation to Temperature: Hot remnants
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GUP: Approximation to Temperature: Hot remnants
Adler, Santiago 1999
Adler, Chen, Santiago 2001

17. GUP: Approximation to Temperature: Hot remnants
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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GUP: Approximation to Temperature: Hot remnants
Adler, Santiago 1999
Adler, Chen, Santiago 2001

18. GUP: Approximation to Temperature: Hot remnants
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP: Approximation to Temperature: Hot remnants
Adler, Santiago 1999
Adler, Chen, Santiago 2001
Hawking temperature
Hot evaporation endpoint

19. GUP: Exploiting a Hilbert space representation
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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GUP: Exploiting a Hilbert space representation
Hilbert space
representation
Kempf, Mangano, Mann 1996

20. GUP: Exploiting a Hilbert space representation
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP: Exploiting a Hilbert space representation
Hilbert space
representation
Kempf, Mangano, Mann 1996
Approximation
in nonlocal Lagrangian
gives nonlocal EFE
Krasnikov 1987,
Modesto 2012, 2013
Moffat 2012
Choose

21. GUP: Exploiting a Hilbert space representation
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP: Exploiting a Hilbert space representation
Hilbert space
representation
Kempf, Mangano, Mann 1996
Approximation
in nonlocal Lagrangian
gives nonlocal EFE
Krasnikov 1987,
Modesto 2012, 2013
Moffat 2012
Choose
Isi, Mureika, Nicolini 2013
Balazin, Nachbagauer 1994
What is the effect on
a Schwarzschild BH?

22. GUP: Exploiting a Hilbert space representation
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP: Exploiting a Hilbert space representation
Hilbert space
representation
Kempf, Mangano, Mann 1996
Approximation
in nonlocal Lagrangian
gives nonlocal EFE
Krasnikov 1987,
Modesto 2012, 2013
Moffat 2012
Choose
Isi, Mureika, Nicolini 2013
Balazin, Nachbagauer 1994
What is the effect on
a Schwarzschild BH?
Modified Newton's
potential

23. GUP: Exploiting a Hilbert space representation
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP: Exploiting a Hilbert space representation
Hilbert space
representation
Kempf, Mangano, Mann 1996
Approximation
in nonlocal Lagrangian
gives nonlocal EFE
Krasnikov 1987,
Modesto 2012, 2013
Moffat 2012
Choose
Isi, Mureika, Nicolini 2013
Balazin, Nachbagauer 1994
What is the effect on
a Schwarzschild BH?
Modified Newton's
potential
Analytical result:

24. GUP inspired Black holes: Self completeness
Isi, Mureika,
Nicolini 2013
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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25. GUP inspired Black holes: Self completeness
Isi, Mureika,
Nicolini 2013
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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26. GUP inspired Black holes: Self completeness
Isi, Mureika,
Nicolini 2013
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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27. GUP inspired Black holes: Self completeness
Isi, Mureika,
Nicolini 2013
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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28. GUP inspired Black holes: Self completeness
Isi, Mureika,
Nicolini 2013
Self complete: Can relate free parameter to fundamental length
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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29. The black hole remnant: thermodynamics inaccessible regime cooldown
Temperature:
The black hole
remnant:
thermodynamics
inaccessible
regime
cooldown
phase
semiclassical regime
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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30. The black hole remnant: thermodynamics inaccessible regime cooldown
Temperature:
The black hole
remnant:
thermodynamics
inaccessible
regime
cooldown
phase
semiclassical regime
Heat
capacity
Phase transition
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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31. The remnant: A cold stable evaporation endpoint The black hole
Temperature:
The black hole
remnant:
thermodynamics
inaccessible
regime
cooldown
phase
semiclassical regime
Heat
capacity
Phase transition
The remnant:
A cold stable
evaporation
endpoint
Entropy
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32. Extension of such models
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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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

33. Adressing the weak hierarchy problem of the Standard Model
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Adressing the weak hierarchy problem of the Standard Model
Elektroweak scale
Planck scale
vs.

34. Large Extra Dimensions
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Large Extra Dimensions
ADD scenario
Integrated huge Volume of
extra dimensions
Large µm up to mm

35. Large Extra Dimensions
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Large Extra Dimensions
Arkani-Hamed
Dimopoulos
Dvali 1998
ADD scenario
Integrated huge Volume of
extra dimensions
Large µm up to mm

36. The Kempf-Mangano-Mann model in N+1 dimensions
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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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 1996
Scardigli, Casadio 2003

37. The Kempf-Mangano-Mann model in N+1 dimensions
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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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 1996
Scardigli, Casadio 2003
We can solve the nonlocal operator analytically in any number of extradimensions

38. GUP-inspired BH in higher dimensions
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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GUP-inspired BH in higher dimensions
One extra dimension

39. GUP-inspired BH in higher dimensions
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP-inspired BH in higher dimensions
One extra dimension
More than one extra dimension

40. GUP-inspired BH in higher dimensions
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP-inspired BH in higher dimensions
One extra dimension
More than one extra dimension
No more remnants in higher (N > 4) dimensions.

41. Retracing a popular Gedankenexperiment
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Retracing a popular Gedankenexperiment
The Heisenberg microscope in n LXDs:
Adler 2010
Carr 2014

42. Retracing a popular Gedankenexperiment
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Retracing a popular Gedankenexperiment
The Heisenberg microscope in n LXDs:
Adler 2010
Carr 2014
This Gedankenexperiment motivates a modified GUP:
Constant integrand: Sounds reasonable
We can solve this spacetime analytically in any dimension.

43. Modified GUP inspired Black Holes
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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Modified GUP inspired Black Holes

44. Modified GUP inspired Black Holes
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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Modified GUP inspired Black Holes
Gravitational potential with 4 extra dimensions:

45. Modified GUP inspired Black Holes
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Modified GUP inspired Black Holes
Gravitational potential with 4 extra dimensions:
Gravitational potential with 1 extra dimension:
Pathologies!

46. GUP in extra dimensions: Ways out
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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GUP in extra dimensions: Ways out

47. GUP in extra dimensions: Ways out
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP in extra dimensions: Ways out
• Improve GUP. Example:
Maziashvili 2013

48. GUP in extra dimensions: Ways out
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
Sven Köppel:
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GUP in extra dimensions: Ways out
• Improve GUP. Example:
Maziashvili 2013
• Improve NLG.
Include higher derivative terms in nonlocal operator

49. GUP in extra dimensions: Ways out
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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GUP in extra dimensions: Ways out
• Improve GUP. Example:
Maziashvili 2013
• Improve NLG.
Include higher derivative terms in nonlocal operator
• Propose nonsingular model.
Model engineering
Hayward 2006

50. Analytical continuation
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Analytical continuation

51. Analytical continuation
Sven Köppel:
Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Analytical continuation
Softening the Ricci curvature scalar divergence
Schwarzschild BH
GUP-inspired BH
Finite curvature BH

52. Analytical continuation
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Sven Köppel: GUP-inspired Black Holes and Extra Dimensions
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Analytical continuation
Softening the Ricci curvature scalar divergence
Schwarzschild BH
GUP-inspired BH
Finite curvature BH
Analytical continuation:

53. The Generalized Uncertainty Principle and Extra Dimensions
Sven Köppel
The Generalized Uncertainty Principle
and Extra Dimensions
Thank you for your attention!
Ongoing
Köppel, Isi, Knipfer, Mureika, Nicolini
Self-Completeness and the GUP
in extradimensions
Köppel, Knipfer, Dirkes, Frassino, Nicolini, Bleicher
GUP and BHs – a pedagogical review
References
Isi, Mureika, Nicolini
Self-Completeness and the GUP
[JHEP 2013]