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Understanding Black Hole Microstates: Introduction to BH Entropy and Entanglement

Explore black hole microstates, entropy, and entanglement in the context of General Relativity, examining the concept of BH entropy, horizon states, and microscopic configurations. Delve into theories like AdS/CFT, String Theory, and Quantized Gravity.

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Understanding Black Hole Microstates: Introduction to BH Entropy and Entanglement

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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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