Non-Supersymmetric Black Holes and Their Microstates

Non-supersymmetric black holes and their microstates

Bert Vercnocke

CEA Saclay

ArXiv: 1109.5180 + 1208.3468 with Iosif Bena and Andrea Puhm (Saclay) 1110.5641 + in progress with Borun Chowdhury (Amsterdam) 1111.2601 + 1206.2349 with Iosif Bena and Hagen Triendl (Saclay)

CERN, 27 November 2012 1. Motivation

2. Black hole microstates and the fuzzball proposal

3. Own work: Microstates for non-extremal black holes

4. Outro 1. Motivation

2. Black hole microstates and the fuzzball proposal

3. Own work: Microstates for non-extremal black holes

4. Outro Motivation

What is a black hole?

I “Region of spacetime from which nothing can escape”

I Black hole uniqueness theorems (Einstein-Maxwell) M, Q, J determine stationary BH completely Motivation

Semiclassical gravity [Hawking] Black hole radiates: Entropy, Temperature

AH SBH = , TH = surface gravity 4GN ‘Bekenstein-Hawking entropy’

Questions:

I Singularity (classical!)

I Entropy

I Information paradox Question 1: Singularity

Classical GR: black hole has a singularity

I “Cosmic censorship”: always hidden by a horizon

I Quantum resolution: near singularity?

Expectation: at least Planck size/string size corrections Question 2: Entropy

Black hole entropy

I One unique BH: NBH = 1

I Boltzmann relation SBH = log Nmicro

1077 Nmicro = e for M

Expectation: ﬁnd ‘microstates’ in quantum gravity/string theory Question 3: Information problem

Information Paradox

I Schwarzschild:

2 AH ∝ M , TH ∝ 1/M

I Positive feedback: black hole radiates away

I Thought experiment: Unitarity lost?

Expectation: quantum corrections such that evolution is unitary Questions, problems, solutions?

Problem set

I Singularity

I Entropy

I Information paradox

Idea

Theoretical test for string theory 1. Motivation

2. Black hole microstates and the fuzzball proposal

3. Own work: Microstates for non-extremal black holes

4. Outro Black hole microstates

Are there N = eSBH “microstates”?

I How to think of such microstates?

I Can they explain more than entropy SBH? Enter string theory! I Charged black hole: gauge ﬁeld Aµ for each brane

Microscopic understanding → microstates?

Black holes in string theory

Black holes from branes

I Wrap branes on internal dimensions at one position in 4d

4d spacetime

I Large number of branes: 4d black hole Black holes in string theory

Black holes from branes

I Wrap branes on internal dimensions at one position in 4d

4d spacetime

I Large number of branes: 4d black hole

I Charged black hole: gauge ﬁeld Aµ for each brane

Microscopic understanding → microstates? Black hole microstates Where are the black hole microstates? String theory since ’95: entropy from counting states in a dual regime for supersymmetric black holes [Strominger, Vafa ’96] + many many others What happens to microstates when gravity is strong?

Black hole microstates

Two shortcomings:

I Supersymmetric:

number of ground states insensitive to value of GN BUT: no radiation, no solution for information problem

I No gravity interpretation of a single microstate Black hole microstates

Two shortcomings:

I Supersymmetric:

number of ground states insensitive to value of GN BUT: no radiation, no solution for information problem

I No gravity interpretation of a single microstate

What happens to microstates when gravity is strong? I Radiation from near-horizon

I Information paradox still there!

Black hole microstates

Naive picture:

I ‘Normal’ objects shrink with increasing GN

I Black hole grows rH = 2GNM Black hole microstates

Naive picture:

I ‘Normal’ objects shrink with increasing GN

I Black hole grows rH = 2GNM

I Radiation from near-horizon

I Information paradox still there! Black hole microstates Observation: Microstates at ﬁnite GN of horizon size

I Black hole near-horizon region changes drastically I Information paradox could be solved Fuzzball/microstate geometries proposal:

For any black hole, there are eSBH horizonless microstates that are solutions to the (string) equations of motion.

Fuzzball proposal

String theory microstates actually grow with GN: “fuzzballs”

I Size of black hole horizon

I No horizon themselves; smooth Fuzzball proposal

String theory microstates actually grow with GN: “fuzzballs”

I Size of black hole horizon

I No horizon themselves; smooth

Fuzzball/microstate geometries proposal:

For any black hole, there are eSBH horizonless microstates that are solutions to the (string) equations of motion. Fuzzball proposal

Consequences of fuzzball/microstate proposal:

I A priori: can be very non-classical!

I Singularity resolution not near singularity, but large scale Common in string theory: [Klebanov-Strassler], D1-D5 [Lunin-Mathur; Lunin, Maldacena, Maoz] Enhanc¸on [Johnson, Peet, Polchinski], [Lin, Lunin, Maldacena]

I Semi-classical gravity cannot be trusted at large scales? See also “ﬁrewall” [Almheiri, Marolf, Polchinski, Sully ’12] Multicenter solutions [Denef ’00, Denef-Bates ’03]

Properties of microstate geometries In this talk: classical fuzzballs or microstate geometries:

I Solutions to supergravity (low-energy string theory)

I Same asymptotic charges as black hole

I No horizon themselves

I Possible due to new couplings in supergravity action Properties of microstate geometries In this talk: classical fuzzballs or microstate geometries:

I Solutions to supergravity (low-energy string theory)

I Same asymptotic charges as black hole

I No horizon themselves

I Possible due to new couplings in supergravity action

Multicenter solutions [Denef ’00, Denef-Bates ’03] “Small” black holes: everything ok

0 I D1-D5 black hole: only horizon after α corrections

I Microstate geometries smooth, no horizon [Lunin,Mathur ’01],[Lunin,Maldacena,Maoz],[Taylor ’05]

I Inﬁnite dimensional family – quantization [Rychkov ’05]: p p SBH = N1N5 , Smicro = N1N5 .

Status of microstate geometries

Supersymmetric Solutions in 5d Supergravity Status of microstate geometries

Supersymmetric Solutions in 5d Supergravity

“Small” black holes: everything ok

0 I D1-D5 black hole: only horizon after α corrections

I Microstate geometries smooth, no horizon [Lunin,Mathur ’01],[Lunin,Maldacena,Maoz],[Taylor ’05]

I Inﬁnite dimensional family – quantization [Rychkov ’05]: p p SBH = N1N5 , Smicro = N1N5 . Status of microstate geometries

“Real” black holes: missing microstates

I Supersymmetric black holes in 4d/5d supergravity

I Microstate geometries no horizon themselves [2005-2008] [Bena,Bobev,Giusto,Ruef,Wang,Warner], [Balasubramanian, Berglund, Gimon, Levi], [Denef, Gaiotto, Strominger, Van den Bleeken, Yin], [de Boer, El-Showk, Messamah, Van den Bleeken],[Saxena,Giusto,Mathur],[Ford,Peet,Potvin,Ross]

I Inﬁnite dimensional family – quantization: [Bena,Bobev,Ruef,Warner ’08],[de Boer, El-Showk, Messamah, Van den Bleeken ’08]

p 3/2 5/4 SBH = N1N5Np ∝ N , Smicro ∝ N .

+ work in progress [Bena, de Boer, Giusto, Shigemori, Warner. . . ] Non-extremal black holes M > Q

Which horizon? Information paradox?

Supersymmetric BH’s are extremal M = Q

Fuzzball: singularity resolution up to horizon size

Status of microstate geometries

Charged black holes → cosmic censorship: M ≥ Q Non-extremal black holes M > Q

Which horizon? Information paradox?

Status of microstate geometries

Charged black holes → cosmic censorship: M ≥ Q

Supersymmetric BH’s are extremal M = Q

Fuzzball: singularity resolution up to horizon size Status of microstate geometries

Charged black holes → cosmic censorship: M ≥ Q

Supersymmetric BH’s are extremal Non-extremal black holes M = Q M > Q

Fuzzball: singularity resolution Which horizon? up to horizon size Information paradox? 1. Motivation

2. Black hole microstates and the fuzzball proposal

3. Own work: Microstates for non-extremal black holes

4. Outro Microstates for non-extremal black holes Overview

a) Microstates are ‘multicenter’ solutions b) Method: one center = probe c) Results + A ∧ F ∧ F

d ? F = F ∧ F ↓

∂rF0r = F12F34

I Charge dissolved in ﬂuxes

I Typical in string theory (ﬂux compactiﬁcations. . . )

Multi-center solutions

Einstein-Maxwell: L5d = ?F ∧ F

I Electric point source for electric ﬁeld A0: d ? F = 0 ↓

∂rF0r = Qδ(~x) I Charge dissolved in ﬂuxes

I Typical in string theory (ﬂux compactiﬁcations. . . )

Multi-center solutions

String theory/supergravity: L5d = ?F ∧ F + A ∧ F ∧ F

I Magnetic ﬁelds F12 and F34 source electric ﬁeld A0: d ? F = 0 d ? F = F ∧ F ↓ ↓

∂rF0r = Qδ(~x) ∂rF0r = F12F34 Multi-center solutions

String theory/supergravity: L5d = ?F ∧ F + A ∧ F ∧ F

I Magnetic ﬁelds F12 and F34 source electric ﬁeld A0: d ? F = 0 d ? F = F ∧ F ↓ ↓

∂rF0r = Qδ(~x) ∂rF0r = F12F34

I Charge dissolved in ﬂuxes

I Typical in string theory (ﬂux compactiﬁcations. . . ) Non-extremal multi-center solutions

Non-supersymmetric black hole microstates

I Extremal: many multi-center solutions (no quantization yet) [Goldstein, Katmadas], [Bena,Dall’Agata, Giusto, Ruef, Warner], [Bossard, Katmadas, Nicolai, Ruef] . . .

I Non-extremal: Only two very non-generic solutions known ‘JMaRT’ [Jejjala, Madden, Ross, Titchener ’05] ‘Running Bolt’ [Bena, Giusto, Ruef, Warner ’08]

Need to understand general non-extremal solutions → HARD! Method: one center = probe

... Non-extremal background [Anninos,Anous,Barandes,Denef,Gaasbeek ’11],[Chowdhury, BV ’11] ... SUSY background, SUSY broken by relative orientation [Bena, Puhm, BV ’11,’12]

Non-extremal multi-center solutions

“Do not pray to the saint who does not help you” [I. Bena] Non-extremal multi-center solutions

“Do not pray to the saint who does not help you” [I. Bena]

Method: one center = probe

... Non-extremal background [Anninos,Anous,Barandes,Denef,Gaasbeek ’11],[Chowdhury, BV ’11] ... SUSY background, SUSY broken by relative orientation [Bena, Puhm, BV ’11,’12] Background

Microstate of SUSY black hole in N = 2 supergravity in 5 dimensions [Breckenridge,Myers,Peet,Vafa ’96]

a) 5d SUSY black hole b) 5d SUSY microstate 2 −2/3 2 1/3 2 ds5 = −(Z1Z2Z3) (dt + k) + (Z1Z2Z3) ds4 I −1 F = d[ZI (dt + k)] J J Z = Q δ(~x) , k = cos2 θ dφ + sin2 θ dφ 4 I I r2 1 r2 2 2

Background a) 5d SUSY black hole

BMPV black hole in 5 dimensions [Breckenridge,Myers,Peet,Vafa ’96]

I 4 Parameters: Q1, Q2, Q3 electric charges |J1| = |J2| 2 angular momenta I String/M-theory interpretation: D1-D5-P or M2-M2-M2 or. . . Background a) 5d SUSY black hole

BMPV black hole in 5 dimensions [Breckenridge,Myers,Peet,Vafa ’96]

I 4 Parameters: Q1, Q2, Q3 electric charges |J1| = |J2| 2 angular momenta I String/M-theory interpretation: D1-D5-P or M2-M2-M2 or. . .

2 −2/3 2 1/3 2 ds5 = −(Z1Z2Z3) (dt + k) + (Z1Z2Z3) ds4 I −1 F = d[ZI (dt + k)] J J Z = Q δ(~x) , k = cos2 θ dφ + sin2 θ dφ 4 I I r2 1 r2 2 2 J K • 4ZI = |IJK|FmagnFmagn 2

I Two new elements: 2 2 • ds4 = dsTaub-NUT −1 2 2 = V (dψ + A) + Vds3

[Bena,Warner 05], [Berglund,Gimon,Levi 06], [Saxena,Potvin,Giusto,Peet 06]

Background b) 5d SUSY microstate

I Microstate: “bubbling geometry” 2 −2/3 2 1/3 2 ds5 = −(Z1Z2Z3) (dt + k) + (Z1Z2Z3) ds4 I −1 I F = d[ZI (dt + k)] + Fmagn J K • 4ZI = |IJK|FmagnFmagn 2 [Bena,Warner 05], [Berglund,Gimon,Levi 06], [Saxena,Potvin,Giusto,Peet 06]

Background b) 5d SUSY microstate

I Microstate: “bubbling geometry” 2 −2/3 2 1/3 2 ds5 = −(Z1Z2Z3) (dt + k) + (Z1Z2Z3) ds4 I −1 I F = d[ZI (dt + k)] + Fmagn

I Two new elements: 2 2 • ds4 = dsTaub-NUT −1 2 2 = V (dψ + A) + Vds3 Background b) 5d SUSY microstate

I Microstate: “bubbling geometry” 2 −2/3 2 1/3 2 ds5 = −(Z1Z2Z3) (dt + k) + (Z1Z2Z3) ds4 I −1 I F = d[ZI (dt + k)] + Fmagn

I Two new elements: 2 2 • ds4 = dsTaub-NUT −1 2 2 = V (dψ + A) + Vds3

J K • 4ZI = |IJK|FmagnFmagn 2 [Bena,Warner 05], [Berglund,Gimon,Levi 06], [Saxena,Potvin,Giusto,Peet 06] If bound state is SUSY, backreaction is known: smooth, no horizon

Probe Supertube: 3 parameters; carries no entropy (single brane with worldvolume ﬂux)

q1, q2 electric charges jtube angular momentum

[d3 = q1q2/jtube dipole charge] Probe Supertube: 3 parameters; carries no entropy (single brane with worldvolume ﬂux)

q1, q2 electric charges jtube angular momentum

[d3 = q1q2/jtube dipole charge]

If bound state is SUSY, backreaction is known: smooth, no horizon I Background with 7 centers on a line [Bena, Wang, Warner ’06]

P P Microstate decays: MADM = I QI + ∆M → MADM = I QI

Probe DBI Potential Interpret Supertube as D4 brane with dissolved D2 and F1: Z p Z SDBI + SWZ = −TD4 − det(g + F) + µD4 (C5 + C3 ∧ F) P P Microstate decays: MADM = I QI + ∆M → MADM = I QI

Probe DBI Potential Interpret Supertube as D4 brane with dissolved D2 and F1: Z p Z SDBI + SWZ = −TD4 − det(g + F) + µD4 (C5 + C3 ∧ F)

I Background with 7 centers on a line [Bena, Wang, Warner ’06] Probe DBI Potential Interpret Supertube as D4 brane with dissolved D2 and F1: Z p Z SDBI + SWZ = −TD4 − det(g + F) + µD4 (C5 + C3 ∧ F)

I Background with 7 centers on a line [Bena, Wang, Warner ’06]

P P Microstate decays: MADM = I QI + ∆M → MADM = I QI R √ I Length of throat L = grrdr Black hole: Microstate:

Probe calculation for many microstates: I We ﬁnd: LBH ≥ LMS , but also LBH < LMS I No dynamical mechanism,

Properties: Singularity resolution?

? Probe calculation for many microstates: I We ﬁnd: LBH ≥ LMS , but also LBH < LMS I No dynamical mechanism,

Properties: Singularity resolution? R √ I Length of throat L = grrdr Black hole: Microstate:

? Properties: Singularity resolution? R √ I Length of throat L = grrdr Black hole: Microstate:

Probe calculation for many microstates: I We ﬁnd: LBH ≥ LMS , but also LBH < LMS I No dynamical mechanism, rd Newton’s 3 law (idea Kachru,Kallosh,Linde,Maldacena,McAllister,Trivedi ’03)

I We ﬁnd at leading order in 1/r expansion: FBH 6= Fmicrostate

Properties: Force on charged particles

I No supergravity description of non-extremal microstate Properties: Force on charged particles

I No supergravity description of non-extremal microstate rd Newton’s 3 law (idea Kachru,Kallosh,Linde,Maldacena,McAllister,Trivedi ’03)

I We ﬁnd at leading order in 1/r expansion: FBH 6= Fmicrostate Non-extremal black hole background

Background: Cvetic-Youm black hole

I 6 Parameters:

Q1, Q2, Q3 electric charges J1, J2 2 indep. angular momenta MADM ADM mass (temperature) Supertubes: Results: the potential Supertube potential

I Supersymmetric limit of background (BMPV) [Marolf,Virmani;Bena,Kraus;Puhm Talk] bgd bgd I (Q1 , Q2 ) = (30, 20), (Q1, Q2) = (1.5, 1.3)

~ H 0.035 J -6 , Q3 0.1 0.030 J 6 , Q 0.1 2 3 ρ? = q1q2 − Q3 J 18 , Q3 1 0.025 ¡ ¡ 0.020 ¡ 0.015 ¡ 0.010 ¡

0.005 ¡ Ρ 0.5 1.0 1.5 Results: the potential

Non-extremal Cvetic-Youm background

I Expect minima to lift

I Parameter M ∼ TBH ∼ ‘mass above extremality’

M 0.01 ~ H 0.035 J -6 , Q3 0.1

0.030 J 6 , Q3 0.1

J 18 , Q3 1 0.025

0.020

0.015

0.010

0.005 Ρ 0.5 1.0 1.5 1. Motivation

2. Black hole microstates and the fuzzball proposal

3. Own work: Microstates for non-extremal black holes

4. Outro Summary Fuzzball proposal and microstate geometries

I (smooth) Horizonless microstates

I Supersymmetric: not enough

I Non-extremal: ‘none’

Non-extremal multi-center bound states?

I Probe supertubes: stable and metastable bound states

I Multi-black holes and microstate geometries Outlook Non-extremal microstate geometries?

I Strange properties (“too deep”, force)

I Full backreacted geometry? Dim. reduction, group theory (long term)

I Will backreaction work? [Work in Progress] cf. problems with anti-D3 brane backreaction [Uppsala,Saclay. . . ] supertubes: more than one charge; smooth object

Firewall of AMPS [Almheiri, Marolf, Polchinski, Sully ’12]

I 1, 2 and 4 are mutually inconsistent

I Give up 4: freely falling observer burns up

back

Firewalls Black Hole complementarity: 4 postulates

1. Distant observer: unitary S-matrix for BH evaporation 2. Semi-classical gravity outside stretched horizon 3. Distant observer: discrete energy levels → entropy 4. Freely falling observer: nothing special crossing the horizon ⇒ Region outside “stretched horizon” describes all physics Firewalls Black Hole complementarity: 4 postulates

Firewall of AMPS [Almheiri, Marolf, Polchinski, Sully ’12]

I 1, 2 and 4 are mutually inconsistent

I Give up 4: freely falling observer burns up

back Our work:

I E < kT: their spacetime ends way before horizon

I Force on probe particles: some fuzzballs are felt far away

back

Firewalls and fuzzballs Situation before AMPS:

I Fuzzballs alter BH geometry: near horizon not vacuum

I Fuzzball complementarity: [Mathur ’12] • E kT quanta go into collective excitations of fuzzballs; experience spacetime “inside” • E ∼ kT exite single fuzzball. Probe non-BH-ness, information of the fuzzball gets encoded in the Hawking radiation Firewalls and fuzzballs Situation before AMPS:

I Fuzzballs alter BH geometry: near horizon not vacuum

Our work:

I E < kT: their spacetime ends way before horizon

I Force on probe particles: some fuzzballs are felt far away

back