Steve Giddings UC, Santa Barbara

Black holes and information — an update

QUANTUM GRAVITY and All of That

Sept. 2, 2021

Funded in part by: US DOE Heising-Simons Foundation I believe (as others likely do) that the problem of BH information is a key problem for quantum gravity, much as understanding the atom played a key role in the development of quantum mechanics

Would like to use it as a guide to new principles of quantum gravity Or possibly observational signatures?

Today: update some perspectives on this There are various perspectives on the problem, as well as proposed resolutions

E.g. a lot of focus on entropy calculations — but entropies are just one diagnostic

A suggested way to organize our understanding of the problem connecting to the information theoretic perspective, focussing on certain questions that may be important:

A “Black Hole Theorem” …

~ Coleman-Mandula? Interesting part is the loophole … “Black Hole Theorem:”

If 1) A BH is a subsystem 2) Distinct BH states have identical exterior evolution 3) BH disappears at end of evolution

Then this violates Quantum Mechanics (unitary evolution)

(applies to other systems)

First, clarify the assumptions … 1) A BH is a subsystem

Bit Colloquially, murky Veer r r ℋ = ℋBH ⊗ ℋenv

Local QFT (LQFT):

|ψBH, ψenv⟩

(or, |ψBH, ψA, ψenv⟩)

“quantum atmosphere”

Hear Operator subalgebras: T $BH, $env commute

Or: |Uϵ⟩: split vacuum

r o r R

LQFT, other quantum systems: subsystem structure hardwired at beginning 2) Distinct BH states have identical exterior evolution

Heir

UH U(t)

Year |ψBH,i, ψenv⟩ → |ψB′ H,i, ψe′nv⟩

r Concrete realization: U(t) from LQFT TBHi Hawking evolution [Recent concrete study: 2006.10834, 2108.07824; D-dim w/J. Perkins, in preparation]

r o r R

To characterize:

ρ Tr ψ t ψ t independent of env = BH | ( )⟩⟨ ( )| ψBH,i (but cutoﬀ dependent) Or: ψ t | |ψ t indep. of ⟨ ( ) (env ( )⟩ ψBH,i for all (env ∈ $env

LQFT: Locality (Ignore grav. backreaction, or semiclassical correction - e.g. CGHS) 3) BH disappears at end of evolution

U(t) |ψBH,i, ψenv⟩ → |ψBH,F, ψe′′n v⟩ independent of i

• Many —> one: U nonunitary; violates QM • One diagnostic:

|ψ ψ | i˜ S ∑ BH,i, env⟩ ⟩ ent ≠ 0 i → 0

Auxiliary system E.g. early Hawking radiation To evade, need to violate one or more assumption

Like with Coleman-Mandula, the loophole may guide new principles…

There are various popular proposed outs.

A good test question: how does your proposal diﬀer from LQFT/Hawking evolution?

(have increasingly detailed story regarding how that works)

[e.g. 2006.10834, 2108.07824, …] E.g. microscopic remnants • Violate assumption 3), disappearance [see e.g. hep-th/9412159, • Introduces other problems, e.g. inﬁnite production Susskind hep-th/9501106]

E.g. massive remnants [hep-th/9203059] e.g. Fuzzball Modify 1) Subsystems Massive Firewall BH (and 2) evolution) remnant Gravastar Planck star M M ≫ Planck etc.

E.g. ’t Hooft’s scenario?

E.g. ER=EPR diﬀerent subsystem identiﬁcation? But how systematically works? E.g. Replica wormholes [Saad, Shenker, Stanford; S Penington, Shenker, Stanford, Yang; a Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini; 8rad + many more ]

Prescription: “diﬀerent saddles”

SBK

Elmo How do we relate this to the standard QM language of states and amplitudes? Or, does it represent a modiﬁcation of QM rules? [some discussion: 2004.02900 w/ Turiaci]

Possible approach: connection to baby universes [Marolf & Maxﬁeld + …]

E.g. Baby Universe

Horizon Black Hole Seems like modiﬁcation of subsystem structure?

Info —> baby universe state?

But, a general approach (in an approximation) [Coleman, SG & Strominger]

H a a† Δ = ( BU,i + BU,i) (i

a a† |α α |α “alpha vacua” ( BU,i + BU,i) i⟩ = i i⟩

• If (i localized inside BH, hard to see how helps - couplings shift, “BH theorem” remains • But, if (i nonlocal on scales ≳ R , can violate assumption 2: Outside evolution can depend on BH state: nonlocal interactions … will return to

Or: some other interpretation ??? What is it? Return to general discussion; back to assumptions How much signiﬁcantly new structure needs to be introduced?

1) A BH is a subsystem 2) Distinct BH states have identical exterior evolution 3) BH disappears at end of evolution

What is a subsystem? An important basic concept

1) Finite (or locally ﬁnite) systems: ℋ = ℋA ⊗ ℋB

Measurement here independent of state here

2) LQFT [e.g. Haag] $ = $1 ∨ $2 ∨ ⋯

J X ⟨J|ϕ(x)|J⟩ = ⟨0|ϕ(x)|0⟩ E.g. r Hawking evolution respects; constrains information escape |J⟩ = e−i∫ J(x)ϕ(x) |0⟩ 3) Gravity E.g. ϕ(x) not gauge invariant doesn’t commute with constraints |J⟩ not gauge invariant not annihilated by constraints 1 Cμ(x) = T μ(x) − G μ(x) (in eﬀective theory: quantum GR) 0 8πG 0 “A particle is inseparable from its gravitational ﬁeld”

Construction: “gravitational dressing” perturbative: g˜μν = gμν + κhμν (solve constraints) background E.g. −i∫ Jϕ ̂ |J⟩ = e |0⟩ → | J ⟩ = (J[ϕ, h] |0⟩ κ2 = 32πG

i∫ Vμ h T [1507.07921, 1805.11095 w/ Donnelly; | J ⟩̂ ≃ e− [ ] 0μ |J⟩ Leading order: 1802.01602 w/Kinsella; i∫ Vμ h T i∫ Vμ h T (̂ ≃ e− [ ] 0μ ( e [ ] 0μ Also recently Chowdhury, Godet, Papadoulki, Raju]

A gravitational dressing Now, for example, ̂ ̂ [1503.08207, [ ( J1 , ( J2] ≠ 0 1507.07921 w/ Donnelly]

A R

And

J |̂ ĥ x | J ̂ |ĥ x | hmLx ⟨ μν( ) ⟩ ≠ ⟨0 μν( ) 0⟩ NJ

So, in what sense does information localize in gravity? (What is a subsystem?)

Looks like a key structural question? Some results: 1) Perturbative dressing can be chosen such that, e.g., depends only on Poincare charges ⟨ J |̂ hμ ν (x )⋯hμ ν (xn)| J ⟩̂ 1 1 1 n n of | J ⟩̂ (xi well outside source region) [1805.11095 w/ Donnelly; 1903.06160] (suggests limited role for “soft hair”)

2) On the other hand, other observables can see | J ⟩̂ from afar. 0 E.g. translation generators: P = PADM[h(∞)] + C μ μ ∫ μ live at ∞! Marolf (AdS): or, simpler: [1706.03104 w/ Donnelly]

a Translate Translate Propagate HADM AdM J P2 s J N r v Observe Observe So, for example,

ADM μ ⟨ J |̂ ((x) eiPμ a | J ⟩̂ depends on J

J OE E.g., at ∂AdS Translates r Adm B So, information delocalized? Notes: 1) Need to have solution of constraints for this to work

2) In general, need nonperturbative solution. E.g. [1802.01602 w/Kinsella, 2004.07843] A A Black Hole Black Hole i∫ J x ϕ x i∫ J x ϕ x e− 1( ) 1( ) e− 2( ) 2( ) (also, large translation needed) 3) Ladda et al 2002.02448 argue extends to perturbative availability; but exp small ∼ e−mx 4) Taking into account limitations — in what sense is information eﬀectively delocalized?? I

I In short, are these eﬀects suﬃcient to communicate information outside a BH and resolve the problem? Or, is new nonperturbative structure needed? (And need to nonperturbatively solve constraints ~ solve problem)

Back to our assumptions: 0) Quantum mechanics 1) A BH is a subsystem 2) Distinct BH states have identical exterior evolution 3) BH disappears at end of evolution

0) QM evolution + 3) disappearance => 1) or 2) (or both) fail: “nonlocality theorem”

What if 1), subsystems, “true to good approximation”? e.g ℋ ≃ ℋBH ⊗ ℋenv

or |Ψ⟩ ≃ |ψBH,i, ψenv⟩

Then: 0) QM + 1) + 3) => Distinct BH states don’t have identical exterior evolution:

[0911.3395, 1108.2015, New BH state-dependent interactions 1211.7070, 1302.2613, 1401.5804, 1701.08765, 1905.08807 + more] Such BH state-dependent interactions violate semiclassical locality

Can explore in a principled “parameterization of ignorance:” [Overview: 1905.08807] Black Hole

|Ψ⟩ ∼ |ψBH,i, ψenv⟩

TBH i OA H = HLQFT + ΔH

Simplest form: H λA env Δ ∼ ∑ ij (A A r R

If ψenv ~ described by LQFT, build from local QFT operators Other points: Expect act on scale ≳ R (compare also wormhole discussion) Natural scale; avoid ﬁrewall Where BH radiation produced (“BH atmosphere”) Reasonable hypothesis: universal coupling Match/maintain thermal properties Gedanken experiments involving “mining” Universality of gravity Can satisfy with:

ΔH = λA dVGμν(x) T (x) ∑ ∫ A μν A

Support on scales r ∼ R

μν μν A μν = dV H (x) Tμν(x) with H (x) = λ G (x) ∫ ∑ A A ~ BH state dependent metric perturbation

Other constraints?

Must transfer information (entanglement): expect need ~1 qubit/R

μν ⟨ψBH, t|H (x)|ψBH, t⟩ = ((1) suﬃcient “strong/coherent”

~ O(1) metric perturbations, possibly visible to e.g. EHT?

[1406.7001, 1703.03387 e.g. time-dependent distortion 1606.07814 w/ Psaltis] now bounded But what size is necessary? General problem: information transfer between subsystems, given couplings [1701.08765; Estimate, ~Fermi’s Golden Rule: 1710.00005 w/Rota]

dI dP ∼ = 2πρ(E )|ΔH|2 dt dt f

S Sbh − bh/2 suﬃces If ρ(Ef ) ∝ e |ΔH| ∼ e

−Sbh/2 I.e. ⟨Hμν(x)⟩ = ((e ) “weak/incoherent”

Harder to see w/ EHT.

But, e.g. grav. wave scattering: [1904.05287]

dP 2 = 2πρ(E )|ΔH|2 dV⟨i|Hμν |ψ⟩⟨β|T |α⟩ dt f ∫ μν

Can be O(1) for wavelengths ~R: Possible modiﬁcation to absorption/reﬂection LIGO/VIRGO/etc. consequences? (being explored) So, to summarize: 0) Quantum mechanics 1) A BH is a subsystem 2) Distinct BH states have identical exterior evolution 3) BH disappears at end of evolution

… inconsistent

- it’s helpful to understand how a given scenario evades this

- the question of subsystems in gravity is an important one — basic structure of QG? Have some results, but also remaining puzzles

- Theorem: if QM, subsystems, and BHs disappear, new interactions

“nonlocal” w.r.t. semiclassical description can parameterize possible observational consequences: EHT, GW detection