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On black hole microstates

On black hole microstates. Amos Yarom. Ram Brustein. Martin Einhorn. Introduction BH entropy Entanglement entropy BH microstates. q. Geometry. General relativity. G mn =T mn. =0. r=2M. Coordinate singularity. r=0. Spacetime singularity. r. y. q. x. Coordinate singularities.

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On black hole microstates

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  1. On black hole microstates Amos Yarom. Ram Brustein. Martin Einhorn. Introduction BH entropy Entanglement entropy BH microstates

  2. q Geometry

  3. General relativity Gmn=Tmn =0 r=2M Coordinate singularity r=0 Spacetime singularity

  4. r y q x Coordinate singularities x=r cos q y=r sin q

  5. r=0 t r=2M x Previous coordinates: x Kruskal extension t=3/2 t=1 t=1/2 t=0

  6. r=0 t r=2M t x Kruskal extension

  7. Black hole thermodynamics S. Hawking (1975) J. Beckenstein (1973) S =0 S  A S = ¼ A TH=1/(8pM)

  8. What does BH entropy mean? • BH Microstates • Horizon states • Entanglement entropy

  9. 1 1 2 2 q Entanglement entropy Results q≠0: 50% ↑ 50% ↓ Results: 50% ↑ 50% ↓

  10. All |↓22↓| elements 1 2 Entanglement entropy S=0 S1=Trace (r1lnr1)=ln2 S2=Trace (r2lnr2)=ln2

  11. The vacuum state r=0 t r=2M x |0

  12. Tr2(y’ y’’ r1(y’1,y’’1) =   Exp[-SE] DfD2 f(x,0+)=y’(x) f(x,0)=y(x) f(x,0+)=y’(x) f(x,0-)=y’’(x) t f(x,0-)=y’’(x) 1 y’1 y’’1 Exp[-SE] Df f(x,0+) = y’1(x)y2(x) y’(x) y’’(x) f(x,0-) = y’’1(x)y2(x) x f(x,0+) = y’1(x) f(x,0-) = y’’1(x) Finding r1

  13. What does BH entropy mean? • BH Microstates • Horizon states • Entanglement entropy t 1 y’1 y’’1 Exp[-SE] Df y’1(x) x y’’1(x) f(x,0+) = y’1(x) √ f(x,0-) = y’’1(x) Finding r1 Kabbat & Strassler (1994), R. Brustein, M. Einhorn and A.Y. (to appear)  ’| e-bH|’’ b=T-1=8pM

  14. Curved spacetime Counting of microstates (Conformal) field theory String theory Quantized gravity

  15. Minkowski space Anti deSitter deSitter AdS/CFT Maldacena (1997) AdS space CFT f O Z(fb=f0) = Exp(f0OdV)

  16. What does BH entropy mean? Anti deSitter +BH CFT • BH Microstates • Horizon states • Entanglement entropy AdS/CFT S/A √ 1/R Free theory: l 0 Semiclassical gravity: R>>a’ √ AdS BH Entropy S. S. Gubser, I. R. Klebanov, and A. W. Peet (1996) , T>0 S=A/3 SBH=A/4

  17. AdS/CFT AdS BH Maldacena (2003) AdS BH CFTCFT, T=0 CFT, T>0 ? |0

  18. BH spacetime Generalization R. Brustein, M. Einhorn and A.Y. (to appear) Field theory

  19. Field theory BH spacetime t 1 y’1 y’’1 Exp[-SE] Df f(x,0+) = y’1(x) f(x,0-) = y’’1(x) Generalization f(r0)=0  ’| e-bH|’’

  20. Field theory BH spacetime BH spacetime Generalization ? /2

  21. BH spacetime Generalization Field theory BH spacetime /2 Field theory  Field theory

  22. Summary • BH entropy is a result of: • Entanglement • Microstates • Counting of states using dual FT’s is consistent with entanglement entropy.

  23. End

  24. Entanglement entropy Srednicki (1993) S1=S2

  25. AdS/CFT (example) Witten (1998) Massless scalar field in AdS An operator O in a CFT Exp( )

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