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Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam - - PowerPoint PPT Presentation
Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam - - PowerPoint PPT Presentation
Quantum Coarse-graining behind black holes Arvin Shahbazi-Moghaddam with Ven Chandrasekaran and Raphael Bousso Berkeley June 4th, 2019 Black hole second law A Black holes are thermodynamic objects with S BH = 4 G Black hole second law
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Black hole second law
More local definition of black holes Marginally trapped surface (θk = 0, θl < 0)
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Black hole second law
Apparent horizons have an area law
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Black hole second law
Apparent horizons have an area law Is A[µ]/4G a coarse-grained entropy?
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Black hole second law
Engelhardt-Wall answered this question [1806.01281]
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Black hole second law
Engelhardt-Wall answered this question [1806.01281] We need a microscopic theory+prescription for coarse-graining
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Black hole second law
Engelhardt-Wall answered this question [1806.01281] We need a microscopic theory+prescription for coarse-graining AdS/CFT!
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Review of Engelhardt-Wall construction
Coarse-graining prescription in AdS/CFT
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Review of Engelhardt-Wall construction
Coarse-graining prescription in AdS/CFT Ryu-Takayanagi prescription SCFT = A[X]
4G
where X is an extremal surface (θk = θl = 0)
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Review of Engelhardt-Wall construction
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Review of Engelhardt-Wall construction
Can show A[X] ≤ A[µ]
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Review of Engelhardt-Wall construction
Can show A[X] ≤ A[µ] Engelhardt-Wall’s explicit construction X was found such that A[X] = A[µ] = ⇒ Scoarse = A[µ]
4G!
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Generalized entropy
Area law can be violated quantum-mechanically! e.g. Hawking evaporation
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Generalized entropy
Area law can be violated quantum-mechanically! e.g. Hawking evaporation Add to the area the entropy of matter outside Sgen[µ] =
A 4G + Sout
Generalized entropy!
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Generalized entropy
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Generalized entropy
Quantum apparent horizons satisfy Sgen law
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Quantum coarse-graining?
Quantum corrected RT formula: SCFT = Sgen[X] X : quantum extremal surface
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Quantum coarse-graining?
Quantum corrected RT formula: SCFT = Sgen[X] X : quantum extremal surface If so, then Scoarse = Sgen[µ]
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Ant conjecture: Energy-minimizing states
Aron Wall’s thought experiment [1701.03196]
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Relative entropy in QFT
Srel(ρ|λ) = tr(ρ log ρ − ρ log σ)
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Relative entropy in QFT
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Relative entropy in QFT
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Ant conjecture: Energy-minimizing states
(There exists a state that satisfies it)
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Ant conjecture: Energy-minimizing states
Let’s go to that state!
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Ant conjecture: Energy-minimizing states
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Ant conjecture: Energy-minimizing states
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Ant conjecture: Energy-minimizing states
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Ant conjecture: Energy-minimizing states
Faulkner-Ceyhan [1812.04683]
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Put them together: quantum coarse-graining
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Put them together: quantum coarse-graining
Sgen[X] = Sgen[µ] = ⇒ Scoarse = Sgen[µ]
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