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 More local definition of black holes Marginally trapped surface ( θ k = 0 , θ l < 0)

Black hole second law Apparent horizons have an area law

Black hole second law Apparent horizons have an area law Is A [ µ ] / 4 G � a coarse-grained entropy?

Black hole second law Engelhardt-Wall answered this question [1806.01281]

Black hole second law Engelhardt-Wall answered this question [1806.01281] We need a microscopic theory+prescription for coarse-graining

Black hole second law Engelhardt-Wall answered this question [1806.01281] We need a microscopic theory+prescription for coarse-graining AdS/CFT!

Review of Engelhardt-Wall construction Coarse-graining prescription in AdS/CFT

Review of Engelhardt-Wall construction Coarse-graining prescription in AdS/CFT Ryu-Takayanagi prescription S CFT = A [ X ] 4 G � where X is an extremal surface ( θ k = θ l = 0)

Review of Engelhardt-Wall construction

Review of Engelhardt-Wall construction Can show A [ X ] ≤ A [ µ ]

Review of Engelhardt-Wall construction Can show A [ X ] ≤ A [ µ ] Engelhardt-Wall’s explicit construction ⇒ S coarse = A [ µ ] X was found such that A [ X ] = A [ µ ] = 4 G � !

Generalized entropy Area law can be violated quantum-mechanically! e.g. Hawking evaporation

Generalized entropy Area law can be violated quantum-mechanically! e.g. Hawking evaporation A Add to the area the entropy of matter outside S gen [ µ ] = 4 G � + S out Generalized entropy!

Generalized entropy

Generalized entropy Quantum apparent horizons satisfy S gen law

Quantum coarse-graining? Quantum corrected RT formula: S CFT = S gen [ X ] X : quantum extremal surface

Quantum coarse-graining? Quantum corrected RT formula: S CFT = S gen [ X ] X : quantum extremal surface If so, then S coarse = S gen [ µ ]

Ant conjecture: Energy-minimizing states Aron Wall’s thought experiment [1701.03196]

Relative entropy in QFT S rel ( ρ | λ ) = tr ( ρ log ρ − ρ log σ )

Relative entropy in QFT

Relative entropy in QFT

Ant conjecture: Energy-minimizing states (There exists a state that satisfies it)

Ant conjecture: Energy-minimizing states Let’s go to that state!

Ant conjecture: Energy-minimizing states

Ant conjecture: Energy-minimizing states

Ant conjecture: Energy-minimizing states

Ant conjecture: Energy-minimizing states Faulkner-Ceyhan [1812.04683]

Put them together: quantum coarse-graining

Put them together: quantum coarse-graining S gen [ X ] = S gen [ µ ] = ⇒ S coarse = S gen [ µ ]

Thank you!