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. FILL 2 ways to understand: AdS-CFT Correspondence Count BH Microstates
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. Black hole regime of parameters:
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. Black hole regime of parameters:
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. Black hole = ensemble of horizonless microstates
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 eS microstates P V = n R T dE = T dS + P dV
Statistical Physics
(Air -- molecules)
eS microstates
typical atypical
Thermodynamics
(Air = ideal gas)
P V = n R T dE = 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 Can be proved by rigorous calculations:
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
∞ 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 Same growth with GN !!!
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-NUT many 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 5D Giusto, 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 smooth low-curvature horizonless solution ?

23. More general solutions
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 !

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
STUBE ~ SBH
ENHANCED

25. Punchline: Typical states grow as GN increases. Horizon never forms.
Black Hole Deconstruction Denef, Gaiotto, Strominger, Van den Bleeken, Yin (2007)
S ~ SBH
Black Holes
Strominger - Vafa S = SBH
Effective coupling ( gs )
Smooth Horizonless Microstate Geometries
Multicenter Quiver QM Denef, 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
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