Black hole thermodynamics

Transcription

1 Black hole thermodynamics Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Spring workshop/kosmologietag, Bielefeld, May 2014 with R. McNees and J. Salzer:

2 Main statements and overview Main statement 1 Black holes are thermal states four laws of black hole mechanics/thermodynamics phase transitions between black holes and vacuum Daniel Grumiller Black hole thermodynamics 2/19

3 Main statements and overview Main statement 1 Black holes are thermal states Main statement 2 Black hole thermodynamics useful for quantum gravity checks quantum gravity entropy matching with semi-classical prediction k B c 3 A h S BH = G }{{ N 4 + O(ln A h) } =1 in this talk semi-classical log corrections of entropy Daniel Grumiller Black hole thermodynamics 2/19

4 Main statements and overview Main statement 1 Black holes are thermal states Main statement 2 Black hole thermodynamics useful for quantum gravity checks Main statement 2 Black hole thermodynamics useful for quantum gravity concepts information loss, fuzzballs, firewalls,... black hole holography, AdS/CFT, gauge/gravity correspondence,... Daniel Grumiller Black hole thermodynamics 2/19

5 Everything is geometry? Gravity at low energies: described by general relativity Daniel Grumiller Black hole thermodynamics 3/19

6 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ Daniel Grumiller Black hole thermodynamics 3/19

7 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ gauge symmetry: diffeomorphisms δ ξ g µν = µ ξ ν + ν ξ µ Daniel Grumiller Black hole thermodynamics 3/19

8 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ gauge symmetry: diffeomorphisms δ ξ g µν = µ ξ ν + ν ξ µ low energy action: Einstein Hilbert S EH 1 d 4 x g (Λ + R) + marginal + irrelevant κ Daniel Grumiller Black hole thermodynamics 3/19

9 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ gauge symmetry: diffeomorphisms δ ξ g µν = µ ξ ν + ν ξ µ low energy action: Einstein Hilbert S EH 1 d 4 x g (Λ + R) + marginal + irrelevant κ basic field equations: Einstein equations R µν = 0 Daniel Grumiller Black hole thermodynamics 3/19

10 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ gauge symmetry: diffeomorphisms δ ξ g µν = µ ξ ν + ν ξ µ low energy action: Einstein Hilbert S EH 1 d 4 x g (Λ + R) + marginal + irrelevant κ basic field equations: Einstein equations R µν = 0 simplest solution: spherically symmetric Schwarzschild BH ds 2 = (1 2M/r) dt 2 + dr 2 /(1 2M/r) + r 2 dω 2 S 2 Daniel Grumiller Black hole thermodynamics 3/19

11 Everything is geometry? Gravity at low energies: described by general relativity basic field: metric g µµ gauge symmetry: diffeomorphisms δ ξ g µν = µ ξ ν + ν ξ µ low energy action: Einstein Hilbert S EH 1 d 4 x g (Λ + R) + marginal + irrelevant κ basic field equations: Einstein equations R µν = 0 simplest solution: spherically symmetric Schwarzschild BH ds 2 = (1 2M/r) dt 2 + dr 2 /(1 2M/r) + r 2 dω 2 S 2 Everything phrased in terms of geometry! Classical gravity = geometry! Daniel Grumiller Black hole thermodynamics 3/19

12 Prehistory 1930ies, TOV: star in hydrostatic equilibrium star = spherically symmetric, self-gravitating perfect fluid with linear equation of state p ρ Daniel Grumiller Black hole thermodynamics 4/19

13 Prehistory 1930ies, TOV: star in hydrostatic equilibrium star = spherically symmetric, self-gravitating perfect fluid with linear equation of state p ρ 1960ies, Zel dovich: bound from causality p ρ causal limit p = ρ: speed of sound = speed of light with hindsight: interesting thermodynamical properties! Daniel Grumiller Black hole thermodynamics 4/19

14 Prehistory 1930ies, TOV: star in hydrostatic equilibrium star = spherically symmetric, self-gravitating perfect fluid with linear equation of state p ρ 1960ies, Zel dovich: bound from causality p ρ causal limit p = ρ: speed of sound = speed of light with hindsight: interesting thermodynamical properties! in particular, entropy is not extensive, S(R) R 3 (R = size) e.g. for p = ρ/3 we get S(R) R 3/2 Daniel Grumiller Black hole thermodynamics 4/19

15 Prehistory 1930ies, TOV: star in hydrostatic equilibrium star = spherically symmetric, self-gravitating perfect fluid with linear equation of state p ρ 1960ies, Zel dovich: bound from causality p ρ causal limit p = ρ: speed of sound = speed of light with hindsight: interesting thermodynamical properties! in particular, entropy is not extensive, S(R) R 3 (R = size) e.g. for p = ρ/3 we get S(R) R 3/2 for causal limit p = ρ: S(R) R 2 area Daniel Grumiller Black hole thermodynamics 4/19

16 Prehistory 1930ies, TOV: star in hydrostatic equilibrium star = spherically symmetric, self-gravitating perfect fluid with linear equation of state p ρ 1960ies, Zel dovich: bound from causality p ρ causal limit p = ρ: speed of sound = speed of light with hindsight: interesting thermodynamical properties! in particular, entropy is not extensive, S(R) R 3 (R = size) e.g. for p = ρ/3 we get S(R) R 3/2 for causal limit p = ρ: Even before Bekenstein Hawking: S(R) R 2 area Non-extensive entropy expected from/predicted by GR! Daniel Grumiller Black hole thermodynamics 4/19

17 Thermodynamics and black holes black hole thermodynamics? Thermodynamics Zeroth law: T = const. in equilibrium Black hole mechanics Zeroth law: κ = const. f. stationary black holes T : temperature κ: surface gravity Daniel Grumiller Black hole thermodynamics 5/19

18 Thermodynamics and black holes black hole thermodynamics? Thermodynamics Zeroth law: T = const. in equilibrium First law: de T ds+ work terms Black hole mechanics Zeroth law: κ = const. f. stationary black holes First law: dm κda+ work terms T : temperature E: energy S: entropy κ: surface gravity M: mass A: area (of event horizon) Daniel Grumiller Black hole thermodynamics 5/19

19 Thermodynamics and black holes black hole thermodynamics? Thermodynamics Zeroth law: T = const. in equilibrium First law: de T ds+ work terms Second law: ds 0 Black hole mechanics Zeroth law: κ = const. f. stationary black holes First law: dm κda+ work terms Second law: da 0 T : temperature E: energy S: entropy κ: surface gravity M: mass A: area (of event horizon) Daniel Grumiller Black hole thermodynamics 5/19

20 Thermodynamics and black holes black hole thermodynamics? Thermodynamics Zeroth law: T = const. in equilibrium First law: de T ds+ work terms Second law: ds 0 Third law: T 0 impossible T : temperature E: energy S: entropy Black hole mechanics Zeroth law: κ = const. f. stationary black holes First law: dm κda+ work terms Second law: da 0 Third law: κ 0 impossible κ: surface gravity M: mass A: area (of event horizon) Formal analogy or actual physics? Daniel Grumiller Black hole thermodynamics 5/19

21 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! Daniel Grumiller Black hole thermodynamics 6/19

22 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! δs Universe < 0 Daniel Grumiller Black hole thermodynamics 6/19

23 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! δs Universe < 0 violates second law of thermodynamics! Daniel Grumiller Black hole thermodynamics 6/19

24 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! δs Universe < 0 violates second law of thermodynamics! Bekenstein: BHs have entropy proportional to area of event horizon! S BH A h Daniel Grumiller Black hole thermodynamics 6/19

25 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! δs Universe < 0 violates second law of thermodynamics! Bekenstein: BHs have entropy proportional to area of event horizon! generalized second law holds: S BH A h δs total = δs Universe + δs BH 0 Daniel Grumiller Black hole thermodynamics 6/19

26 Bekenstein Hawking entropy Gedankenexperiment by Wheeler: throw cup of lukewarm tea into BH! δs Universe < 0 violates second law of thermodynamics! Bekenstein: BHs have entropy proportional to area of event horizon! S BH A h generalized second law holds: δs total = δs Universe + δs BH 0 Hawking: indeed! S BH = 1 4 A h using semi-classical gravity Daniel Grumiller Black hole thermodynamics 6/19

27 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Daniel Grumiller Black hole thermodynamics 7/19

28 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Slick shortcut: Euclidean BHs! (t E : Euclidean time) ds 2 = (1 2M/r) dt 2 E + dr 2 /(1 2M/r) + irrelevant Daniel Grumiller Black hole thermodynamics 7/19

29 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Slick shortcut: Euclidean BHs! (t E : Euclidean time) ds 2 = (1 2M/r) dt 2 E + dr 2 /(1 2M/r) + irrelevant near horizon approximation: r = 2M + x 2 /(8M) ds 2 = x 2 dt 2 E 16M 2 + dx2 + irrelevant Daniel Grumiller Black hole thermodynamics 7/19

30 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Slick shortcut: Euclidean BHs! (t E : Euclidean time) ds 2 = (1 2M/r) dt 2 E + dr 2 /(1 2M/r) + irrelevant near horizon approximation: r = 2M + x 2 /(8M) ds 2 = x 2 dt 2 E 16M 2 + dx2 + irrelevant conical singularity at x = 0, unless t E t E + 8πM = t E + β Daniel Grumiller Black hole thermodynamics 7/19

31 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Slick shortcut: Euclidean BHs! (t E : Euclidean time) ds 2 = (1 2M/r) dt 2 E + dr 2 /(1 2M/r) + irrelevant near horizon approximation: r = 2M + x 2 /(8M) ds 2 = x 2 dt 2 E 16M 2 + dx2 + irrelevant conical singularity at x = 0, unless t E t E + 8πM = t E + β periodicity in Euclidean time = inverse temperature Daniel Grumiller Black hole thermodynamics 7/19

32 Hawking temperature Hawking effect from QFT on fixed (curved) background: particle production with thermal spectrum at Hawking temperature Slick shortcut: Euclidean BHs! (t E : Euclidean time) ds 2 = (1 2M/r) dt 2 E + dr 2 /(1 2M/r) + irrelevant near horizon approximation: r = 2M + x 2 /(8M) ds 2 = x 2 dt 2 E 16M 2 + dx2 + irrelevant conical singularity at x = 0, unless t E t E + 8πM = t E + β periodicity in Euclidean time = inverse temperature Result: Hawking temperature! T H = 1 8πM Daniel Grumiller Black hole thermodynamics 7/19

33 Free energy from Euclidean path integral Main idea Consider Euclidean path integral (Gibbons, Hawking, 1977) ( Z = DgDX exp 1 ) I E[g, X] Daniel Grumiller Black hole thermodynamics 8/19

34 Free energy from Euclidean path integral Main idea Consider Euclidean path integral (Gibbons, Hawking, 1977) ( Z = DgDX exp 1 ) I E[g, X] g: metric, X: scalar field Daniel Grumiller Black hole thermodynamics 8/19

35 Free energy from Euclidean path integral Main idea Consider Euclidean path integral (Gibbons, Hawking, 1977) ( Z = DgDX exp 1 ) I E[g, X] g: metric, X: scalar field Semiclassical limit ( 0): dominated by classical solutions (?) Daniel Grumiller Black hole thermodynamics 8/19

36 Free energy from Euclidean path integral Main idea Consider Euclidean path integral (Gibbons, Hawking, 1977) ( Z = DgDX exp 1 ) I E[g, X] g: metric, X: scalar field Semiclassical limit ( 0): dominated by classical solutions (?) Exploit relationship between Z and Euclidean partition function Z e β Ω Ω: thermodynamic potential for appropriate ensemble β: periodicity in Euclidean time Daniel Grumiller Black hole thermodynamics 8/19

37 Free energy from Euclidean path integral Main idea Consider Euclidean path integral (Gibbons, Hawking, 1977) ( Z = DgDX exp 1 ) I E[g, X] g: metric, X: scalar field Semiclassical limit ( 0): dominated by classical solutions (?) Exploit relationship between Z and Euclidean partition function Z e β Ω Ω: thermodynamic potential for appropriate ensemble β: periodicity in Euclidean time Requires periodicity in Euclidean time and accessibility of semi-classical approximation Daniel Grumiller Black hole thermodynamics 8/19

38 Free energy from Euclidean path integral Semiclassical Approximation Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] =I E [g cl, X cl ] + δi E [g cl, X cl ; δg, δx] δ2 I E [g cl, X cl ; δg, δx] +... Daniel Grumiller Black hole thermodynamics 9/19

39 Free energy from Euclidean path integral Semiclassical Approximation Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] =I E [g cl, X cl ] + δi E [g cl, X cl ; δg, δx] δ2 I E [g cl, X cl ; δg, δx] +... The leading term is the on-shell action. Daniel Grumiller Black hole thermodynamics 9/19

40 Free energy from Euclidean path integral Semiclassical Approximation Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] =I E [g cl, X cl ] + δi E [g cl, X cl ; δg, δx] δ2 I E [g cl, X cl ; δg, δx] +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. Daniel Grumiller Black hole thermodynamics 9/19

41 Free energy from Euclidean path integral Semiclassical Approximation Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] =I E [g cl, X cl ] + δi E [g cl, X cl ; δg, δx] δ2 I E [g cl, X cl ; δg, δx] +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. The quadratic term represents the first corrections. Daniel Grumiller Black hole thermodynamics 9/19

42 Free energy from Euclidean path integral Semiclassical Approximation Consider small perturbation around classical solution I E [g cl + δg, X cl + δx] =I E [g cl, X cl ] + δi E [g cl, X cl ; δg, δx] δ2 I E [g cl, X cl ; δg, δx] +... The leading term is the on-shell action. The linear term should vanish on solutions g cl and X cl. The quadratic term represents the first corrections. If nothing goes wrong: ( Z exp 1 ) I E[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 I E... Daniel Grumiller Black hole thermodynamics 9/19

43 Free energy from Euclidean path integral What could go Wrong? Accessibility of the semiclassical approximation requires Daniel Grumiller Black hole thermodynamics 10/19

44 Free energy from Euclidean path integral What could go Wrong? Accessibility of the semiclassical approximation requires 1. I E [g cl, X cl ] > Typical gravitational actions evaluated on black hole solutions: 1. Violated: Action unbounded from below Daniel Grumiller Black hole thermodynamics 10/19

45 Free energy from Euclidean path integral What could go Wrong? Accessibility of the semiclassical approximation requires 1. I E [g cl, X cl ] > 2. δi E [g cl, X cl ; δg, δx] = 0 Typical gravitational actions evaluated on black hole solutions: 1. Violated: Action unbounded from below 2. Violated: First variation of action not zero for all field configurations contributing to path integral due to boundary terms Daniel Grumiller Black hole thermodynamics 10/19

46 Free energy from Euclidean path integral What could go Wrong? Accessibility of the semiclassical approximation requires 1. I E [g cl, X cl ] > 2. δi E [g cl, X cl ; δg, δx] = 0 Typical gravitational actions evaluated on black hole solutions: 1. Violated: Action unbounded from below 2. Violated: First variation of action not zero for all field configurations contributing to path integral due to boundary terms δi EOM E dx [ ] γ π ab δγ ab + π X δx 0 M Daniel Grumiller Black hole thermodynamics 10/19

47 Free energy from Euclidean path integral What could go Wrong?...everything! Accessibility of the semiclassical approximation requires 1. I E [g cl, X cl ] > 2. δi E [g cl, X cl ; δg, δx] = 0 3. δ 2 I E [g cl, X cl ; δg, δx] 0 Typical gravitational actions evaluated on black hole solutions: 1. Violated: Action unbounded from below 2. Violated: First variation of action not zero for all field configurations contributing to path integral due to boundary terms δi EOM E dx [ ] γ π ab δγ ab + π X δx 0 M 3. Frequently violated: Gaussian integral may diverge Daniel Grumiller Black hole thermodynamics 10/19

48 Free energy from Euclidean path integral What could go Wrong?...everything! Accessibility of the semiclassical approximation requires 1. I E [g cl, X cl ] > 2. δi E [g cl, X cl ; δg, δx] = 0 3. δ 2 I E [g cl, X cl ; δg, δx] 0 Typical gravitational actions evaluated on black hole solutions: 1. Violated: Action unbounded from below 2. Violated: First variation of action not zero for all field configurations contributing to path integral due to boundary terms δi EOM E dx [ ] γ π ab δγ ab + π X δx 0 M 3. Frequently violated: Gaussian integral may diverge Holographic renormalization resolves first and second problem! Daniel Grumiller Black hole thermodynamics 10/19

49 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Daniel Grumiller Black hole thermodynamics 11/19

50 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Z g cl ( exp 1 ) Γ[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 Γ... Daniel Grumiller Black hole thermodynamics 11/19

51 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Z g cl ( exp 1 ) Γ[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 Γ... Leading term is finite Daniel Grumiller Black hole thermodynamics 11/19

52 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Z g cl ( exp 1 ) Γ[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 Γ... Leading term is finite Linear term vanishes Daniel Grumiller Black hole thermodynamics 11/19

53 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Z g cl ( exp 1 ) Γ[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 Γ... Leading term is finite Linear term vanishes Quadratic term ok in AdS Daniel Grumiller Black hole thermodynamics 11/19

54 Free energy from Euclidean path integral Holographic renormalization Subtract suitable boundary terms from the action Γ = I E I CT such that second problem resolved; typically also resolves first problem Z g cl ( exp 1 ) Γ[g cl, X cl ] ( Dδg DδX exp 1 ) 2 δ2 Γ... Leading term is finite Linear term vanishes Quadratic term ok in AdS Leading order (set = 1): Here F is the Helmholtz free energy Z(T, X) = e Γ(T, X) βf (T, X) = e Daniel Grumiller Black hole thermodynamics 11/19

55 Example: Hawking Page phase transition of AdS 3 /BTZ Euclidean action: I E = d 3 x g ( R + 2 ) + 2 d 2 x γ K Daniel Grumiller Black hole thermodynamics 12/19

56 Example: Hawking Page phase transition of AdS 3 /BTZ Euclidean action: I E = d 3 x g ( R + 2 ) + 2 d 2 x γ K Holographic counterterm: I CT = 2 d 2 x γ Daniel Grumiller Black hole thermodynamics 12/19

57 Example: Hawking Page phase transition of AdS 3 /BTZ Euclidean action: I E = d 3 x g ( R + 2 ) + 2 d 2 x γ K Holographic counterterm: I CT = 2 d 2 x γ (Euclidean) AdS 3 (t E t E + β, ϕ ϕ + 2π) yields free energy ds 2 = cosh 2 ρ dt 2 E + sinh 2 ρ dϕ 2 + dρ 2 F AdS = 1 8 Daniel Grumiller Black hole thermodynamics 12/19

58 Example: Hawking Page phase transition of AdS 3 /BTZ Euclidean action: I E = d 3 x g ( R + 2 ) + 2 d 2 x γ K Holographic counterterm: I CT = 2 d 2 x γ (Euclidean) AdS 3 (t E t E + β, ϕ ϕ + 2π) yields free energy (non-rotating) BTZ BH ds 2 = cosh 2 ρ dt 2 E + sinh 2 ρ dϕ 2 + dρ 2 F AdS = 1 8 ds 2 = (r 2 r+) 2 dt 2 + dr2 r 2 r+ 2 + r 2 dϕ 2 yields free energy (T = r + /(2π)) F BTZ = π2 T 2 2 = 1 8 T 2 T 2 crit. Daniel Grumiller Black hole thermodynamics 12/19

59 Example: Hawking Page phase transition of AdS 3 /BTZ Euclidean action: I E = d 3 x g ( R + 2 ) + 2 d 2 x γ K Holographic counterterm: I CT = 2 d 2 x γ (Euclidean) AdS 3 (t E t E + β, ϕ ϕ + 2π) yields free energy (non-rotating) BTZ BH ds 2 = cosh 2 ρ dt 2 E + sinh 2 ρ dϕ 2 + dρ 2 F AdS = 1 8 ds 2 = (r 2 r+) 2 dt 2 + dr2 r 2 r+ 2 + r 2 dϕ 2 yields free energy (T = r + /(2π)) F BTZ = π2 T 2 2 = 1 8 T 2 T 2 crit. Critical Hawking Page temperature: T crit. = 1/(2π) Daniel Grumiller Black hole thermodynamics 12/19

60 Works also for flat space and expanding universe (in 2+1) Bagchi, Detournay, Grumiller & Simon PRL 13 Hot flat space (ϕ ϕ + 2π) ds 2 = dt 2 + dr 2 + r 2 dϕ 2 Daniel Grumiller Black hole thermodynamics 13/19

61 Works also for flat space and expanding universe (in 2+1) Bagchi, Detournay, Grumiller & Simon PRL 13 Hot flat space (ϕ ϕ + 2π) ds 2 = dt 2 + dr 2 + r 2 dϕ 2 ds 2 = dτ 2 + (Eτ)2 dx (Eτ) 2 + ( 1 + (Eτ) 2) ( dy + (Eτ)2 1 + (Eτ) 2 dx) 2 Flat space cosmology (y y + 2πr 0 ) Daniel Grumiller Black hole thermodynamics 13/19

62 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Daniel Grumiller Black hole thermodynamics 14/19

63 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Daniel Grumiller Black hole thermodynamics 14/19

64 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Black hole holography Daniel Grumiller Black hole thermodynamics 14/19

65 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Black hole holography Microscopic entropy matching via Cardy formula Daniel Grumiller Black hole thermodynamics 14/19

66 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Black hole holography Microscopic entropy matching via Cardy formula Black hole complementarity and firewalls Daniel Grumiller Black hole thermodynamics 14/19

67 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Black hole holography Microscopic entropy matching via Cardy formula Black hole complementarity and firewalls Everything is information? Daniel Grumiller Black hole thermodynamics 14/19

68 Summary, outlook and rest of the talk (if time permits) Summary: Black hole are thermal states Calculation of free energy requires holographic renormalization Interesting phase transitions possible Generalizable to (flat space) cosmologies Regarding the other two main points: Black hole thermodynamics useful for quantum gravity checks/concepts Information loss? Black hole holography Microscopic entropy matching via Cardy formula Black hole complementarity and firewalls Everything is information? Daniel Grumiller Black hole thermodynamics 14/19

69 Holography Main idea aka gauge/gravity duality, aka AdS/CFT correspondence One of the most fruitful ideas in contemporary theoretical physics: The number of dimensions is a matter of perspective Daniel Grumiller Black hole thermodynamics 15/19

70 Holography Main idea aka gauge/gravity duality, aka AdS/CFT correspondence One of the most fruitful ideas in contemporary theoretical physics: The number of dimensions is a matter of perspective We can choose to describe the same physical situation using two different formulations in two different dimensions Daniel Grumiller Black hole thermodynamics 15/19

71 Holography Main idea aka gauge/gravity duality, aka AdS/CFT correspondence One of the most fruitful ideas in contemporary theoretical physics: The number of dimensions is a matter of perspective We can choose to describe the same physical situation using two different formulations in two different dimensions The formulation in higher dimensions is a theory with gravity The formulation in lower dimensions is a theory without gravity Daniel Grumiller Black hole thermodynamics 15/19

72 Why gravity? The holographic principle in black hole physics Boltzmann/Planck: entropy of photon gas in d spatial dimensions S gauge volume L d Bekenstein/Hawking: entropy of black hole in d spatial dimensions S gravity area L d 1 Daniel Grumiller Black hole thermodynamics 16/19

73 Why gravity? The holographic principle in black hole physics Boltzmann/Planck: entropy of photon gas in d spatial dimensions S gauge volume L d Bekenstein/Hawking: entropy of black hole in d spatial dimensions S gravity area L d 1 Daring idea by t Hooft/Susskind (1990ies): Any consistent quantum theory of gravity could/should have a holographic formulation in terms of a field theory in one dimension lower Daniel Grumiller Black hole thermodynamics 16/19

74 Why gravity? The holographic principle in black hole physics Boltzmann/Planck: entropy of photon gas in d spatial dimensions S gauge volume L d Bekenstein/Hawking: entropy of black hole in d spatial dimensions S gravity area L d 1 Daring idea by t Hooft/Susskind (1990ies): Any consistent quantum theory of gravity could/should have a holographic formulation in terms of a field theory in one dimension lower Ground-breaking discovery by Maldacena (1997): Holographic principle is realized in string theory in specific way Daniel Grumiller Black hole thermodynamics 16/19

75 Why gravity? The holographic principle in black hole physics Boltzmann/Planck: entropy of photon gas in d spatial dimensions S gauge volume L d Bekenstein/Hawking: entropy of black hole in d spatial dimensions S gravity area L d 1 Daring idea by t Hooft/Susskind (1990ies): Any consistent quantum theory of gravity could/should have a holographic formulation in terms of a field theory in one dimension lower Ground-breaking discovery by Maldacena (1997): e.g. Holographic principle is realized in string theory in specific way T µν gauge = Tµν BY δ(gravity action) = d d x h T BY µν δh µν Daniel Grumiller Black hole thermodynamics 16/19

76 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Daniel Grumiller Black hole thermodynamics 17/19

77 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Daniel Grumiller Black hole thermodynamics 17/19

78 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Daniel Grumiller Black hole thermodynamics 17/19

79 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Strongly coupled gauge theories (difficult) mapped to semi-cassical gravity (simple) Daniel Grumiller Black hole thermodynamics 17/19

80 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Strongly coupled gauge theories (difficult) mapped to semi-cassical gravity (simple) Quantum gravity (difficult) mapped to weakly coupled gauge theories (simple) Daniel Grumiller Black hole thermodynamics 17/19

81 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Strongly coupled gauge theories (difficult) mapped to semi-cassical gravity (simple) Quantum gravity (difficult) mapped to weakly coupled gauge theories (simple) Examples of first type: heavy ion collisions at RHIC and LHC, superfluidity, high T c superconductors (?), cold atoms (?), strange metals (?),... Daniel Grumiller Black hole thermodynamics 17/19

82 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Strongly coupled gauge theories (difficult) mapped to semi-cassical gravity (simple) Quantum gravity (difficult) mapped to weakly coupled gauge theories (simple) Examples of first type: heavy ion collisions at RHIC and LHC, superfluidity, high T c superconductors (?), cold atoms (?), strange metals (?),... Examples of the second type: microscopic understanding of black holes, information paradox, 3D quantum gravity, flat space holography, non-ads holography, higher-spin holography,... Daniel Grumiller Black hole thermodynamics 17/19

83 Why should I care?...and why were there > 9700 papers on holography in the past 17 years? Many applications! Tool for calculations Strongly coupled gauge theories (difficult) mapped to semi-cassical gravity (simple) Quantum gravity (difficult) mapped to weakly coupled gauge theories (simple) Examples of first type: heavy ion collisions at RHIC and LHC, superfluidity, high T c superconductors (?), cold atoms (?), strange metals (?),... Examples of the second type: microscopic understanding of black holes, information paradox, 3D quantum gravity, flat space holography, non-ads holography, higher-spin holography,... We can expect many new applications in the next decade! Daniel Grumiller Black hole thermodynamics 17/19

84 Thanks for your attention! Daniel Grumiller Black hole thermodynamics 18/19

85 References D. Grumiller, R. McNees and J. Salzer, Black hole thermodynamics The first half century, [arxiv: [gr-qc]]. H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller and J. Rosseel, Higher spin theory in 3-dimensional flat space, Phys. Rev. Lett. 111 (2013) [arxiv: [hep-th]]. A. Bagchi, S. Detournay, D. Grumiller and J. Simon, Cosmic evolution from phase transition of 3-dimensional flat space, Phys. Rev. Lett. 111 (2013) [arxiv: [hep-th]]. A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) [arxiv: [hep-th]]. Thanks to Bob McNees for providing the L A TEX beamerclass! Daniel Grumiller Black hole thermodynamics 19/19