Black Hole Microstates, and the Information Paradox

Iosif Bena

IPhT (SPhT), CEA Saclay

WithWith Nick Warner,Nick Warner, Clement Ruef, Nikolay BobevClement Ruef, Nikolay Bobev andand Stefano GiustoStefano Giusto

Strominger and Vafa (1996)+1000 other articles

Count BH Microstates Match B.H. entropy !!!Match B.H. entropy !!!

2 ways to understand:

Zero GravityFinite Gravity

AdS-CFTCorrespondence

FILL

Strominger and Vafa (1996):Count Black Hole Microstates (branes + strings) Correctly match B.H. entropy !!!Correctly match B.H. entropy !!!

Black hole regime of parameters:

Zero Gravity

Standard lore:As gravity becomes stronger,- brane configuration becomes smaller- horizon develops and engulfs it- recover standard black hole

SusskindHorowitz, Polchinski Damour, Veneziano

Black hole regime of parameters:

Identical to black hole far away. HorizonHorizon →→ Smooth capSmooth cap

Giusto, Mathur, SaxenaBena, Warner

Berglund, Gimon, Levi

Strominger and Vafa (1996):Count Black Hole Microstates (branes + strings) Correctly match B.H. entropy !!!Correctly match B.H. entropy !!!

Zero Gravity

BIG QUESTION:BIG QUESTION: Are all black hole microstates becoming geometries with no horizon ?

Black holeBlack hole = = ensemble of horizonless microstatesensemble of horizonless microstates??

Mathur & friends

ThermodynamicsThermodynamics

Black Hole SolutionBlack Hole Solution

Statistical PhysicsStatistical Physics

Microstate geometriesMicrostate geometries

ThermodynamicsThermodynamics

(Air = (Air = ideal gasideal gas))P V = n R TP V = n R T

dE = T dS + P dVdE = T dS + P dV

Statistical PhysicsStatistical Physics

(Air -- (Air -- moleculesmolecules))eS microstates microstatestypical typical atypicalatypical

Long distance physicsGravitational lensing

Physics at horizonInformation loss

Analogy with ideal gasAnalogy with ideal gas

- Thermodynamics (LQF- Thermodynamics (LQF T) T) breaks down at horizon. Nonlocal effects take over.

- No spacetime inside black holes. Quantum Quantum superposition superposition of microstate geometries.

A few corollairesA few corollaires

Can be proved by rigorous calculations:Can be proved by rigorous calculations:

1. Build most generic microstates + Count

2. Use AdS-CFT ∞ parametersparametersblack hole chargesblack hole charges

new low-mass new low-mass degrees of freedomdegrees of freedom

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)

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

Microstates geometries

Want solutions with same asymptotics, but no horizon

3-charge 5D black hole Strominger, Vafa; BMPV

Microstates geometries

Bena, Warner Gutowski, Reall

Charge coming from fluxes

Microstates geometriesLinear system

4 layers:

Focus on Gibbons-Hawking (Taub-NUT) base:

8 harmonic functions

Bena, Warner

Gauntlett, Gutowski, Bena, Kraus, Warner

Ex: Black Rings (in Taub-NUT)

Elvang, Emparan, Mateos, Reall; Bena, Kraus, Warner; Gaiotto, Strominger, Yin

Explicit example of BH uniqueness violation in 5DBPS Black Saturns, even with BH away from BR centerBena, Wang, Warner

Giusto, Mathur, SaxenaBena, Warner Berglund, Gimon, Levi

Microstates geometries

Compactified to 4D → multicenter configuration

Abelian worldvolume flux Each: 16 supercharges

4 common supercharges

Microstates geometries

Multi-center Taub-NUTmany 2-cycles + flux

• 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 + …

magnetic

Microstates geometries2-cycles + magnetic flux

Charge disolved in fluxesKlebanov-Strassler

A problem ?• Hard to get microstates of realreal 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 > 0, Q1 Q2 Q3 > J2)

Microstates for S>0 black holes

Microstates for S>0 black holes

Microstates for S>0 black holes

Microstates for S>0 black holes

Bena, Wang, Warner

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 ?

• Spectral flow: Bena, Bobev, Warner

GH solution solution with 2-charge supertube in GH background

• Supertubes Mateos, Townsend

– supersymmetric brane configurations– arbitrary shape:– smooth supergravity solutions

Lunin, Mathur; Lunin, Maldacena, Maoz

• Classical moduli space of microstates solutions has infinite dimension !

More general solutions

More general solutionsProblem: 2-charge supertubes have 2 charges

Marolf, Palmer; Rychkov

Solution:

• In deep scaling solutions: Bena, Bobev, Ruef, Warner

• Entropy enhancement !!!

smooth sugra solutions SSTUBETUBE ~ ~ SSBHBH

SSTUBETUBE <<<< SSBHBH

ENHANCEDENHANCED

TUBETUBE

Effective coupling ( gs )

Black HolesStrominger - Vafa

S = SBH

Multicenter Quiver QMDenef, Moore (2007)

S ~ SBH

Black Hole DeconstructionDenef, Gaiotto, Strominger, Van den Bleeken, Yin (2007)

S ~ SBH

Size grows

No Horizon

Smooth Horizonless Microstate Geometries

Punchline:Punchline: Typical states Typical states growgrow as G as GNN increases. increases.

Horizon never forms.Horizon never forms.

Same ingredients: Scaling solutionsScaling solutions of primitiveprimitive centers

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

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

• 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 ?

Black Holes in AdS-CFT: Option 2

• 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

Black Holes in AdS-CFT: Option 3

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

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

Extremal Black Holes • This is not so strange

• Time-like singularity resolved by stringy low-mass modes extending to horizon

What about nonextremal ?• Given total energy budget:

most entropy obtained by making brane-antibrane pairs

• S=2N11/2 + N1

1/2N21/2 + N2

1/2N31/2 + N3

1/2 Horowitz, Maldacena, Strominger

• Mass gap = 1/N1N2N3

• Extend on long distances (horizon scale)

• More mass – lower mass-gap – larger size

Experimental Consequences ?Experimental Consequences ?New light degrees of freedom at horizon.

(independent of string theory)

BH collisions:

- gravity waves – LISA

- primordial BH formation

- continuous spectrum - democratic decay82% hadrons, 18% leptons

- continuous spectrum

- non-democraticnon-democratic decay

LHC: Black Holes vs. Microstates

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