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Black Hole Microstates, and the Information Paradox

Black Hole Microstates, and the Information Paradox. Iosif Bena IPhT (SPhT), CEA Saclay. With Nick Warner, Clement Ruef, Nikolay Bobev and Stefano Giusto. Strominger and Vafa (1996) +1000 other articles Count BH Microstates Match B.H. entropy !!!. 2 ways to understand:. Finite Gravity.

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Black Hole Microstates, and the Information Paradox

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  1. Black Hole Microstates, and the Information Paradox Iosif Bena IPhT (SPhT), CEA Saclay WithNick Warner,Clement Ruef, Nikolay BobevandStefano Giusto

  2. Strominger and Vafa (1996) +1000 other articles Count BH Microstates Match B.H. entropy !!! 2 ways to understand: Finite Gravity Zero Gravity FILL AdS-CFT Correspondence

  3. Strominger and Vafa (1996): Count Black Hole Microstates (branes + strings) Correctly match B.H. entropy !!! Zero Gravity Black hole regime of parameters: • Standard lore: • As gravity becomes stronger,- brane configuration becomes smaller • horizon develops and engulfs it • recover standard black hole Susskind Horowitz, Polchinski Damour, Veneziano

  4. Strominger and Vafa (1996): Count Black Hole Microstates (branes + strings) Correctly match B.H. entropy !!! Zero Gravity Black hole regime of parameters: Identical to black hole far away. Horizon→Smooth cap Giusto, Mathur, Saxena Bena, Warner Berglund, Gimon, Levi

  5. BIG QUESTION:Are allblack hole microstates becoming geometries with no horizon ? Black hole = ensemble of horizonless microstates ? Mathur & friends

  6. Analogy with ideal gas Statistical Physics (Air -- molecules) eS microstates typical atypical Thermodynamics (Air = ideal gas) P V = n R TdE = T dS + P dV Thermodynamics Black Hole Solution Statistical Physics Microstate geometries Long distance physics Gravitational lensing Physics at horizon Information loss

  7. A few corollaires new low-mass degrees of freedom - Thermodynamics (LQFT) breaks down at horizon. Nonlocal effects take over. - No spacetime inside black holes. Quantum superposition of microstate geometries. Can be proved by rigorous calculations: 1. Build most generic microstates + Count 2. UseAdS-CFT ∞ parameters black hole charges

  8. Question • Can a large blob of stuff replace BH ? • Sure !!! • AdS-QCD • Plasma ball dual to BH in the bulk • Recover all BH properties • Absorption of incoming stuff • Hawking radiation • Key ingredient: large number of degrees of freedom (N2)

  9. Word of caution • To replace classical BH by BH-sized object • Gravastar • Fuzzball • LQG muck • Quark-star, you name it … satisfy very stringent (mutilating) test: Horowitz • BH size grows with GN • Size of objects in other theories becomes smaller Same growth with GN !!! - BH microstate geometries pass this test - Highly nontrivial mechanism

  10. Microstates geometries 3-charge 5D black hole Strominger, Vafa; BMPV Want solutions with same asymptotics, but no horizon

  11. Microstates geometries Bena, Warner Gutowski, Reall

  12. Microstates geometries Linear system 4 layers: Charge coming from fluxes Bena, Warner Focus on Gibbons-Hawking (Taub-NUT) base: 8 harmonic functions Gauntlett, Gutowski, Bena, Kraus, Warner

  13. Ex: Black Rings (in Taub-NUT) Elvang, Emparan, Mateos, Reall; Bena, Kraus, Warner; Gaiotto, Strominger, Yin Explicit example of BH uniqueness violation in 5D BPS Black Saturns, even with BH away from BR center Bena, Wang, Warner

  14. Microstates geometries Giusto, Mathur, Saxena Bena, Warner Berglund, Gimon, Levi

  15. Microstates geometries Multi-centerTaub-NUTmany 2-cycles+flux Compactified to 4D → multicenter configuration Abelian worldvolume flux Each: 16 supercharges 4 common supercharges

  16. Microstates geometries 2-cycles + magnetic flux • Where is the BH charge ? L = qA0 L = … + A0F12 F23 + … • Where is theBH mass ? E= … + F12F12+ … • BH angular momentum J = ExB=…+F01F12 +… magnetic Charge disolved in fluxes Klebanov-Strassler

  17. A problem ? • Hard to get microstates of realblack holes • All known solutions • D1 D5 system Mathur, Lunin, Maldacena, Maoz, Taylor, Skenderis • 3-charge (D1 D5P) microstates in 5DGiusto, Mathur, Saxena; Bena, Warner; Berglund, Gimon, Levi • 4-charge microstates in 4D Bena, Kraus; Saxena Potvin, Giusto, Peet • Nonextremal microstates Jejjala, Madden, Ross, Titchener (JMaRT); Giusto, Ross, Saxena did not have charge/mass/J of black hole with classically large event horizon (S > 0, Q1 Q2 Q3 >J2)

  18. Microstates for S>0 black holes

  19. Microstates for S>0 black holes

  20. Microstates for S>0 black holes

  21. Microstates for S>0 black holes Bena, Wang, Warner

  22. Deep microstates • Deeper throat; similar cap ! • Solution smooth throughout scaling • Scaling goes on forever !!! • Can quantum effects stop that ? • Can they destroy huge chunk of smoothlow-curvature horizonless solution ?

  23. More general solutions • Spectral flow: Bena, Bobev, WarnerGH solution solution with 2-charge supertube in GH background • Supertubes Mateos, Townsend • supersymmetric brane configurations • arbitrary shape: • smoothsupergravity solutionsLunin, Mathur; Lunin, Maldacena, Maoz • Classical moduli space of microstates solutions has infinite dimension !

  24. More general solutions Problem: 2-charge supertubes have 2 charges Marolf, Palmer; Rychkov Solution: • In deep scaling solutions: Bena, Bobev, Ruef, Warner • Entropy enhancement !!! smooth sugra solutions STUBE<<SBH TUBE ENHANCED STUBE ~ SBH

  25. Black Hole DeconstructionDenef, Gaiotto, Strominger, Van den Bleeken, Yin (2007) S ~ SBH Black Holes Strominger - Vafa S = SBH Effectivecoupling (gs) Smooth Horizonless Microstate Geometries Multicenter Quiver QMDenef, Moore (2007) S ~ SBH Size grows No Horizon Same ingredients: Scaling solutions of primitive centers Punchline: Typical states grow as GN increases. Horizon never forms.

  26. A bit of AdS-CFT • Every asymptotically AdS microstate geometry dual to a microstate of the boundary CFT • CFT has typical sector (where the states giving BH entropy live) and atypical sectors. • Calculate mass gap of microstate geometries + match with CFT mass gap. • Deep microstates ↔ CFT states intypical sector ! Holographic anatomy Taylor, Skenderis

  27. Black Holes in AdS-CFT: Option 1 • Each state has horizonless bulk dual Mathur • Classical BH solution = thermodynamic approximation • Lots of microstates; dual to CFT states in typicalsector • Size grows with BH horizon. • Finite mass-gap - agrees with CFT expectation Maldacena • Natural continuation of Denef-Moore, DGSVY

  28. Black Holes in AdS-CFT: Option 2 • Typical CFT states have no individual bulk duals. • Many states mapped into one BH solution • Some states in typical CFT sector do have bulk duals. • 1 to 1 map in all other understood systems (D1-D5, LLM, Polchinski-Strassler). Why different ?

  29. Black Holes in AdS-CFT: Option 3 • Typical states have bulk duals with horizon (~ BH) • States in the typical sector of CFT have both infinite and finite throats. • CFT microstates have mass-gap and Heisenberg recurrence. Would-be bulk solutions do not. Maldacena; Balasubramanian, Kraus, Shigemori

  30. Punchline In string theory: BPS extremal black holes = ensembles of horizonless microstates. • Can be proven (disproven) rigorously • No spacetime inside horizon. Instead – quantum superposition of microstates • No unitarity loss/information paradox

  31. Always asked question: • Why are quantum effects affecting the horizon (low curvature) ? • Answer: space-time has singularity: • low-mass degrees of freedom • change the physics on long distances • This is very common in string theory !!! • Polchinski-Strassler • Giant Gravitons + LLM • It can be even worse – quantum effects significant even without horizon de Boer, El Showk, Messamah, van den Bleeken

  32. Extremal Black Holes • This is not so strange • Time-like singularity resolved by stringy low-mass modes extending to horizon

  33. What about nonextremal ? • Given total energy budget: most entropy obtained by making brane-antibrane pairs • S=2p (N11/2 + N11/2)(N21/2 + N21/2)(N31/2 + N31/2)Horowitz, Maldacena, Strominger • Mass gap = 1/N1N2N3 • Extend on long distances (horizon scale) • More mass – lower mass-gap – larger size

  34. Experimental Consequences ? New light degrees of freedom at horizon.(independent of string theory) BH collisions: - gravity waves – LISA • primordial BH formation - continuous spectrum - democratic decay 82% hadrons, 18% leptons - continuous spectrum - non-democratic decay LHC: Black Holes vs. Microstates

  35. Summary and Future Directions • Strong evidence that in string theory:BPS extremal black holes = ensembles of microstates • One may not care about extremal BH’s • One may not care about string theory • Lesson is generic: QG low-mass modes can change physics on large (horizon) scales • Extend to non-extremal black holes • Probably; at least near-extremal • Need more non-extremal microstates • Only one solution known. Works very nicely. Jejjala Madden Ross Titchener (JMaRT); Myers & al, Mathur & al. • Inverse scattering methods. Use JMaRT as seed. • New light degrees of freedom. Experiment ? • LISA: horizon ring-down • LHC: non-democratic decay • Supermassive BH’s easier to form by mergers

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