Black Holes in Nuclear and Particle Physics

Transcription

1 Black Holes in Nuclear and Particle Physics Daniel Grumiller Center for Theoretical Physics Massachusetts Institute of Technology and Institute for Theoretical Physics Vienna University of Technology Annual meeting of the Austrian Physical Society, Aflenz, Austria, September 2008

2 Outline Black Holes in Gravitational Physics Black Holes in Non-Gravitational Physics Case Study: Holographic Renormalization D. Grumiller Black Holes in Nuclear and Particle Physics 2/21

3 Outline Black Holes in Gravitational Physics Black Holes in Non-Gravitational Physics Case Study: Holographic Renormalization D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 3/21

4 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

5 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

6 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! S. Hawking (1975): If Black Holes do exist Kip (Thorne) will get one year of Penthouse. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

7 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! S. Hawking (1975): If Black Holes do exist Kip (Thorne) will get one year of Penthouse. M. Veltman (1994): Black holes are probably nothing else but commercially viable figments of the imagination. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

8 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! S. Hawking (1975): If Black Holes do exist Kip (Thorne) will get one year of Penthouse. M. Veltman (1994): Black holes are probably nothing else but commercially viable figments of the imagination. G. t Hooft (2004): It is however easy to see that such a position is untenable. (comment on Veltman) D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

9 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! S. Hawking (1975): If Black Holes do exist Kip (Thorne) will get one year of Penthouse. M. Veltman (1994): Black holes are probably nothing else but commercially viable figments of the imagination. G. t Hooft (2004): It is however easy to see that such a position is untenable. (comment on Veltman) S. Hughes (2008): Unambiguous observational evidence for the existence of black holes has not yet been established. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

10 Black Holes: A Brief History of Quotes J. Michell (1783):... all light emitted from such a body would be made to return towards it by its own proper gravity. A. Eddington (1935): I think there should be a law of Nature to prevent a star from behaving in this absurd way! S. Hawking (1975): If Black Holes do exist Kip (Thorne) will get one year of Penthouse. M. Veltman (1994): Black holes are probably nothing else but commercially viable figments of the imagination. G. t Hooft (2004): It is however easy to see that such a position is untenable. (comment on Veltman) S. Hughes (2008): Unambiguous observational evidence for the existence of black holes has not yet been established. S. Hughes (2008): Most physicists and astrophysicists accept the hypothesis that the most massive, compact objects seen in many astrophysical systems are described by the black hole solutions of general relativity. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 4/21

11 Why Study Black Holes? Depending whom you ask you ll hear: Mathematician: because they are interesting String Theoretician: because they hold the key to quantum gravity General Relativist: because they are unavoidable Particle Speculator: because they might be produced at LHC Nuclear Physicist: because they are dual to a strongly coupled plasma Astrophysicist: because they explain the data Cosmologist: because they exist But... D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 5/21

12 Why Study Black Holes? Depending whom you ask you ll hear: Mathematician: because they are interesting String Theoretician: because they hold the key to quantum gravity General Relativist: because they are unavoidable Particle Speculator: because they might be produced at LHC Nuclear Physicist: because they are dual to a strongly coupled plasma Astrophysicist: because they explain the data Cosmologist: because they exist But... Do they exist? D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 5/21

13 Why Study Black Holes? Depending whom you ask you ll hear: Mathematician: because they are interesting String Theoretician: because they hold the key to quantum gravity General Relativist: because they are unavoidable Particle Speculator: because they might be produced at LHC Nuclear Physicist: because they are dual to a strongly coupled plasma Astrophysicist: because they explain the data Cosmologist: because they exist But... Do they exist? Let me answer this without getting philosophical, by appealing to data D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 5/21

14 Some Black Hole Observational Data OJ287, about 18 billion solar masses Microscopic BHs: none Primordial BHs: none (upper bound) Stellar mass BHs in binary systems: many (17 good candidates (including Cygnus X-1), 37 other candidates) Isolated stellar mass BHs: some (1 good candidate, 3 other candidates) Intermediate mass BHs: some (11 candidates) Galactic core BHs: many (Milky Way, 66 other candidates) Data compiled in 2004 by R. Johnston Artistic impression (NASA Outreach), presented at the Annual meeting of the American Astronomical Society, 2008 D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 6/21

15 Some Black Hole Observational Data OJ287, about 18 billion solar masses Microscopic BHs: none Primordial BHs: none (upper bound) Stellar mass BHs in binary systems: many (17 good candidates (including Cygnus X-1), 37 other candidates) Isolated stellar mass BHs: some (1 good candidate, 3 other candidates) Intermediate mass BHs: some (11 candidates) Galactic core BHs: many (Milky Way, 66 other candidates) Data compiled in 2004 by R. Johnston Artistic impression (NASA Outreach), presented at the Annual meeting of the American Astronomical Society, 2008 Black holes are the simplest explanation of data! Thus, by Occam s razor they exist. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Gravitational Physics 6/21

16 Outline Black Holes in Gravitational Physics Black Holes in Non-Gravitational Physics Case Study: Holographic Renormalization D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 7/21

17 Black Holes in Science Fiction All I am going to say about this topic is: D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 8/21

18 Black Holes in Science Fiction All I am going to say about this topic is: D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 8/21

19 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part I: Picture Hydraulic jump as a white hole analog Some literature: C. Barcelo, S. Liberati, M. Visser, gr-qc/ G. Volovik, gr-qc/ T. Philbin et al, arxiv: M. Visser, S. Weinfurtner, arxiv: Picture by Piotr Pieranski, taken from a paper by G. Volovik D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 9/21

20 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part II: Formulas Idea: Linearize perturbations in continuity equation and Euler equation t ρ + (ρv) = 0 ρ ( t v + (v )v ) = p and assume no vorticity, v = φ, and barotropic equation of state h = 1 ρ p Then the velocity-potential φ obeys the relativistic (!) wave-equation φ = 1 ( µ gg µν ν φ ) = 0 g with the acoustic metric ( (c 2 v 2 ) v T ) g µν (t, x) = ρ c v I where the speed of sound is given by c 2 = ρ/ p. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 10/21

21 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but... D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

22 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

23 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. Summary Black hole analogs are very useful for pedagogic demonstrations (high schools and undergraduate curriculi!) D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

24 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. Summary Black hole analogs are very useful for pedagogic demonstrations (high schools and undergraduate curriculi!) Workers in the field frequently express the hope to experimentally establish the Hawking effect D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

25 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. Summary Black hole analogs are very useful for pedagogic demonstrations (high schools and undergraduate curriculi!) Workers in the field frequently express the hope to experimentally establish the Hawking effect Even if this works it is not clear what it would teach us D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

26 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. Summary Black hole analogs are very useful for pedagogic demonstrations (high schools and undergraduate curriculi!) Workers in the field frequently express the hope to experimentally establish the Hawking effect Even if this works it is not clear what it would teach us But it would be a cool experiment! D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

27 Condensed Matter Analogs Deaf and Dumb holes (W. Unruh 1981), Part III: Reality Check Black hole analogs are nice, but......they do not necessarily teach us anything new. Summary Black hole analogs are very useful for pedagogic demonstrations (high schools and undergraduate curriculi!) Workers in the field frequently express the hope to experimentally establish the Hawking effect Even if this works it is not clear what it would teach us But it would be a cool experiment! Q: Are there other unexpected applications of black holes? D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 11/21

28 AdS/CFT Correspondence! Relates strings on AdS to specific gauge theories at the boundary of AdS Applications RHIC physics Black hole physics Scattering at strong coupling Cold atoms Superconductors Quantum gravity... to be discovered! Note: J. Maldacena s paper hep-th/ second most cited paper ever (SPIRES). First is Steven Weinberg s A Model of Leptons. D. Grumiller Black Holes in Nuclear and Particle Physics Black Holes in Non-Gravitational Physics 12/21

29 Outline Black Holes in Gravitational Physics Black Holes in Non-Gravitational Physics Case Study: Holographic Renormalization D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 13/21

30 AdS 2... the simplest gravity model where the need for holographic renormalization arises! Bulk action: I B = 1 2 d 2 x g [X ( R + 2 ) ] l 2 M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 14/21

31 AdS 2... the simplest gravity model where the need for holographic renormalization arises! Bulk action: I B = 1 d 2 x g [X ( R + 2 ) ] 2 M l 2 Variation with respect to scalar field X yields R = 2 l 2 This means curvature is constant and negative, i.e., AdS 2. D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 14/21

32 AdS 2... the simplest gravity model where the need for holographic renormalization arises! Bulk action: I B = 1 d 2 x g [X ( R + 2 ) ] 2 M l 2 Variation with respect to scalar field X yields R = 2 l 2 This means curvature is constant and negative, i.e., AdS 2. Variation with respect to metric g yields µ ν X g µν X + g µν X l 2 = 0 D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 14/21

33 AdS 2... the simplest gravity model where the need for holographic renormalization arises! Bulk action: I B = 1 d 2 x g [X ( R + 2 ) ] 2 M l 2 Variation with respect to scalar field X yields R = 2 l 2 This means curvature is constant and negative, i.e., AdS 2. Variation with respect to metric g yields µ ν X g µν X + g µν X l 2 = 0 Equations of motion above solved by X = r, g µν dx µ dx ν = ( r 2 l 2 M) dt 2 + dr2 r 2 l 2 M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 14/21

34 AdS 2... the simplest gravity model where the need for holographic renormalization arises! Bulk action: I B = 1 d 2 x g [X ( R + 2 ) ] 2 M l 2 Variation with respect to scalar field X yields R = 2 l 2 This means curvature is constant and negative, i.e., AdS 2. Variation with respect to metric g yields µ ν X g µν X + g µν X l 2 = 0 Equations of motion above solved by X = r, g µν dx µ dx ν = ( r 2 l 2 M) dt 2 + dr2 r 2 l 2 M There is an important catch, however: Boundary terms tricky! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 14/21

35 Boundary terms, Part I Gibbons Hawking York boundary terms: quantum mechanical toy model Let us start with an bulk Hamiltonian action I B = t f dt [ ṗq H(q, p)] D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 15/21

36 Boundary terms, Part I Gibbons Hawking York boundary terms: quantum mechanical toy model Let us start with an bulk Hamiltonian action I B = t f dt [ ṗq H(q, p)] Want to set up a Dirichlet boundary value problem q = fixed at t f D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 15/21

37 Boundary terms, Part I Gibbons Hawking York boundary terms: quantum mechanical toy model Let us start with an bulk Hamiltonian action I B = t f dt [ ṗq H(q, p)] Want to set up a Dirichlet boundary value problem q = fixed at t f Problem: δi B = 0 requires q δp = 0 at boundary D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 15/21

38 Boundary terms, Part I Gibbons Hawking York boundary terms: quantum mechanical toy model Let us start with an bulk Hamiltonian action I B = t f dt [ ṗq H(q, p)] Want to set up a Dirichlet boundary value problem q = fixed at t f Problem: δi B = 0 requires q δp = 0 at boundary Solution: add Gibbons Hawking York boundary term I E = I B + I GHY, I GHY = pq t f D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 15/21

39 Boundary terms, Part I Gibbons Hawking York boundary terms: quantum mechanical toy model Let us start with an bulk Hamiltonian action I B = t f dt [ ṗq H(q, p)] Want to set up a Dirichlet boundary value problem q = fixed at t f Problem: δi B = 0 requires q δp = 0 at boundary Solution: add Gibbons Hawking York boundary term I E = I B + I GHY, I GHY = pq t f As expected I E = t f dt[p q H(q, p)] is standard Hamiltonian action D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 15/21

40 Boundary terms, Part II Gibbons Hawking York boundary terms in gravity something still missing! That was easy! In gravity the result is I GHY = dx γ X K where γ (K) is determinant (trace) of first (second) fundamental form. Euclidean action with correct boundary value problem is M I E = I B + I GHY The boundary lies at r = r 0, with r 0. Are we done? D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 16/21

41 Boundary terms, Part II Gibbons Hawking York boundary terms in gravity something still missing! That was easy! In gravity the result is I GHY = dx γ X K where γ (K) is determinant (trace) of first (second) fundamental form. Euclidean action with correct boundary value problem is M I E = I B + I GHY The boundary lies at r = r 0, with r 0. Are we done? No! Serious Problem! Variation of I E yields δi E EOM + δx(boundary term) lim dt δγ r M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 16/21

42 Boundary terms, Part II Gibbons Hawking York boundary terms in gravity something still missing! That was easy! In gravity the result is I GHY = dx γ X K where γ (K) is determinant (trace) of first (second) fundamental form. Euclidean action with correct boundary value problem is M I E = I B + I GHY The boundary lies at r = r 0, with r 0. Are we done? No! Serious Problem! Variation of I E yields δi E EOM + δx(boundary term) lim dt δγ r M Asymptotic metric: γ = r 2 /l 2 + O(1). Thus, δγ may be finite! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 16/21

43 Boundary terms, Part II Gibbons Hawking York boundary terms in gravity something still missing! That was easy! In gravity the result is I GHY = dx γ X K where γ (K) is determinant (trace) of first (second) fundamental form. Euclidean action with correct boundary value problem is M I E = I B + I GHY The boundary lies at r = r 0, with r 0. Are we done? No! Serious Problem! Variation of I E yields δi E EOM + δx(boundary term) lim dt δγ r M Asymptotic metric: γ = r 2 /l 2 + O(1). Thus, δγ may be finite! δi E 0 for some variations that preserve boundary conditions!!! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 16/21

44 Boundary terms, Part III Holographic renormalization: quantum mechanical toy model Key observation: Dirichlet boundary problem not changed under I E Γ = I E I CT = I EH + I GHY I CT with I CT = S(q, t) t f D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 17/21

45 Boundary terms, Part III Holographic renormalization: quantum mechanical toy model Key observation: Dirichlet boundary problem not changed under I E Γ = I E I CT = I EH + I GHY I CT with Improved action: I CT = S(q, t) t f Γ = t f dt [ ṗq H(q, p)] + pq t f S(q, t) t f D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 17/21

46 Boundary terms, Part III Holographic renormalization: quantum mechanical toy model Key observation: Dirichlet boundary problem not changed under I E Γ = I E I CT = I EH + I GHY I CT with Improved action: I CT = S(q, t) t f Γ = t f dt [ ṗq H(q, p)] + pq t f S(q, t) t f First variation: δγ EOM = ( p ) S(q, t) q f δq t = 0? D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 17/21

47 Boundary terms, Part III Holographic renormalization: quantum mechanical toy model Key observation: Dirichlet boundary problem not changed under I E Γ = I E I CT = I EH + I GHY I CT with Improved action: I CT = S(q, t) t f Γ = t f dt [ ṗq H(q, p)] + pq t f S(q, t) t f First variation: δγ EOM = ( p ) S(q, t) q f δq t = 0? Works if S(q, t) is Hamilton s principal function! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 17/21

48 Boundary terms, Part IV Holographic renormalization in AdS 2 gravity Hamilton s principle function Solves the Hamilton Jacobi equation Does not change boundary value problem when added to action Is capable to render δγ = 0 even when δi E 0 Reasonable Ansatz: Holographic counterterm = Solution of Hamilton Jacobi equation! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 18/21

49 Boundary terms, Part IV Holographic renormalization in AdS 2 gravity Hamilton s principle function Solves the Hamilton Jacobi equation Does not change boundary value problem when added to action Is capable to render δγ = 0 even when δi E 0 Reasonable Ansatz: Holographic counterterm = Solution of Hamilton Jacobi equation! In case of AdS 2 gravity this Ansatz yields I CT = dx γ X l M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 18/21

50 Boundary terms, Part IV Holographic renormalization in AdS 2 gravity Hamilton s principle function Solves the Hamilton Jacobi equation Does not change boundary value problem when added to action Is capable to render δγ = 0 even when δi E 0 Reasonable Ansatz: Holographic counterterm = Solution of Hamilton Jacobi equation! In case of AdS 2 gravity this Ansatz yields I CT = dx γ X l Action consistent with boundary value problem and variational principle: Γ = 1 d 2 x [ g X ( R + 2 ) ] 2 l 2 dx γ X K + dx γ X l M M M M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 18/21

51 Boundary terms, Part IV Holographic renormalization in AdS 2 gravity Hamilton s principle function Solves the Hamilton Jacobi equation Does not change boundary value problem when added to action Is capable to render δγ = 0 even when δi E 0 Reasonable Ansatz: Holographic counterterm = Solution of Hamilton Jacobi equation! In case of AdS 2 gravity this Ansatz yields I CT = dx γ X l Action consistent with boundary value problem and variational principle: Γ = 1 d 2 x [ g X ( R + 2 ) ] 2 l 2 dx γ X K + dx γ X l M M M M δγ = 0 for all variations that preserve the boundary conditions! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 18/21

52 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

53 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

54 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

55 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp I E [g cl, X cl ]... D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

56 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp I E [g cl, X cl ]... Accessibility of the semi-classical approximation requires 1. I E [g cl, X cl ] > 2. δi E [g cl, X cl ; δg, δx] = 0 D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

57 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp I E [g cl, X cl ]... Accessibility of the semi-classical approximation requires 1. I E [g cl, X cl ] violated in AdS gravity! 2. δi E [g cl, X cl ; δg, δx] = 0 D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

58 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp I E [g cl, X cl ]... Accessibility of the semi-classical approximation requires 1. I E [g cl, X cl ] violated in AdS gravity! 2. δi E [g cl, X cl ; δg, δx] 0 violated in AdS gravity! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

59 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] = I E [g cl, X cl ] + δi E +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp I E [g cl, X cl ]... Accessibility of the semi-classical approximation requires 1. I E [g cl, X cl ] violated in AdS gravity! 2. δi E [g cl, X cl ; δg, δx] 0 violated in AdS gravity! Everything goes wrong with I E! In particular, do not get correct free energy F = T I E = or entropy S = D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

60 Thermodynamics of Black Holes as a Simple Application Consider small perturbation around classical solution Γ[g cl + δg, X cl + δx] = Γ[g cl, X cl ] + δγ +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. If nothing goes wrong get partition function ( ) Z exp Γ[g cl, X cl ]... Accessibility of the semi-classical approximation requires 1. Γ[g cl, X cl ] > ok in AdS gravity! 2. δγ[g cl, X cl ; δg, δx] = 0 ok in AdS gravity! Everything works with Γ! In particular, do get correct free energy F = T I E = M T S and entropy S = 2πX horizon = Area/4 D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 19/21

61 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

62 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

63 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

64 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

65 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle If necessary, subtract holographic counterterm I CT D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

66 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle If necessary, subtract holographic counterterm I CT Use improved action for applications! Γ = I B + I GHY I CT D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

67 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle If necessary, subtract holographic counterterm I CT Use improved action for applications! Γ = I B + I GHY I CT Applications include thermodynamics from Euclidean path integral and calculation of holographic stress tensor in AdS/CFT δγ d n x γ T EOM ab δγ ab T ab = T ab M D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

68 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle If necessary, subtract holographic counterterm I CT Use improved action for applications! Γ = I B + I GHY I CT Applications include thermodynamics from Euclidean path integral and calculation of holographic stress tensor in AdS/CFT δγ d n x γ T EOM ab δγ ab T ab = T ab M Straightforward applications in quantum field theory? D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

69 Summary and algorithm of holographic renormalization In any dimension, for any asymptotics may arise also in quantum field theory! Start with bulk action I B Check consistency of boundary value problem If necessary, add boundary term I GHY Check consistency of variational principle If necessary, subtract holographic counterterm I CT Use improved action for applications! Γ = I B + I GHY I CT Applications include thermodynamics from Euclidean path integral and calculation of holographic stress tensor in AdS/CFT δγ d n x γ T EOM ab δγ ab T ab = T ab M Straightforward applications in quantum field theory? Possibly! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 20/21

70 ... and thanks to my collaborators! Some literature on AdS 2 holography D. Grumiller and R. McNees, JHEP 0704, 074 [arxiv:hep-th/ ]. T. Hartman and A. Strominger, Central charge for AdS 2 quantum gravity, [arxiv: [hep-th]]. M. Alishahiha and F. Ardalan, Central charge for 2D gravity on AdS 2 and AdS 2 /CFT 1 correspondence, [arxiv: [hep-th]]. R. Gupta and A. Sen, AdS(3)/CFT(2) to AdS(2)/CFT(1), [arxiv: [hep-th]]. A. Castro, D. Grumiller, R. McNees and F. Larsen, Holographic description of AdS 2 black holes, [arxiv: [hep-th]]. Thank you for your attention! Thanks to Bob McNees for providing the LATEX beamerclass! D. Grumiller Black Holes in Nuclear and Particle Physics Case Study: Holographic Renormalization 21/21