The Generalized Uncertainty Principle and Extra Dimensions

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Presentation transcript:

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

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

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

Motivation: Why minimal length physics? Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 4 / Motivation: Why minimal length physics? Aurilia, Spallucci 2002 Dvali, Gomez 2010 Carr 2014 UV-Complete Gravity, Minimal length

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

Motivation: Why minimal length physics? Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 6 / 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

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

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

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

Quantum black holes in nature? Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 10 / 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

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

Effective quantum gravity equations Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 12 / 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

A quantum theory of gravity must be nonlocal Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 13 / 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

The Generalized Uncertainty Principle Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 14 / 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 Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 15 / 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

GUP: Approximation to Temperature: Hot remnants Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 16 / GUP: Approximation to Temperature: Hot remnants Adler, Santiago 1999 Adler, Chen, Santiago 2001

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

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

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

GUP: Exploiting a Hilbert space representation Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 20 / 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

GUP: Exploiting a Hilbert space representation Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 21 / 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?

GUP: Exploiting a Hilbert space representation Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 22 / 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

GUP: Exploiting a Hilbert space representation Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 23 / 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:

GUP inspired Black holes: Self completeness Isi, Mureika, Nicolini 2013 Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 24 /

GUP inspired Black holes: Self completeness Isi, Mureika, Nicolini 2013 Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 25 /

GUP inspired Black holes: Self completeness Isi, Mureika, Nicolini 2013 Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 26 /

GUP inspired Black holes: Self completeness Isi, Mureika, Nicolini 2013 Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 27 /

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 28 /

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: 29 /

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 30 /

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 31 /

Extension of such models Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 32 / 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

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

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

Large Extra Dimensions Sven Köppel: GUP-inspired Black Holes and Extra Dimensions Sven Köppel: 35 / Large Extra Dimensions Arkani-Hamed Dimopoulos Dvali 1998 ADD scenario Integrated huge Volume of extra dimensions Large µm up to mm

The Kempf-Mangano-Mann model in N+1 dimensions Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 36 / 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

The Kempf-Mangano-Mann model in N+1 dimensions Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 37 / 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

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

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

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

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

Retracing a popular Gedankenexperiment Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 42 / 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.

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

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

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

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

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

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

GUP in extra dimensions: Ways out Sven Köppel: Sven Köppel: GUP-inspired Black Holes and Extra Dimensions 49 / 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

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

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

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

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]