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Black Hole Microstates, and the Information Paradox

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Title: Black Hole Microstates, and the Information Paradox


1
Black Hole Microstates, and the Information
Paradox
  • Iosif Bena
  • IPhT (SPhT), CEA Saclay

With Nick Warner, Clement Ruef, Nikolay Bobev and
Stefano 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 all black 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 (LQF T) 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. Use AdS-CFT
8 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-center Taub-NUTmany 2-cycles flux
Compactified to 4D ? multicenter configuration
Abelian worldvolume flux Each 16 supercharges
4 common supercharges
16
Microstates geometries
  • Where is the BH charge ?
  • L q A0
  • L A0 F12 F23
  • Where is the BH mass ?
  • E F12 F12
  • BH angular momentum
  • J E x B F01 F12

2-cycles magnetic flux
magnetic
Charge disolved in fluxes Klebanov-Strassler
17
A problem ?
  • Hard to get microstates of real black holes
  • All known solutions
  • D1 D5 system Mathur, Lunin, Maldacena, Maoz,
    Taylor, Skenderis
  • 3-charge (D1 D5 P) 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 gt 0, Q1 Q2 Q3
    gt J2)

18
Microstates for Sgt0 black holes
19
Microstates for Sgt0 black holes
20
Microstates for Sgt0 black holes
21
Microstates for Sgt0 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 smooth
    low-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
  • smooth supergravity 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 ltlt SBH
TUBE
ENHANCED
STUBE SBH
25
Black Hole DeconstructionDenef, Gaiotto,
Strominger, Van den Bleeken, Yin (2007) S SBH
Black Holes
Strominger - Vafa S SBH
Effective coupling ( 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 in typical 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
    typical sector
  • 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
  • S2p (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 BHs
  • 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 BHs easier to form by mergers

36
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