ERC AdG 692951-GravBHs

Based on
2012.07821 [hep-th] w/
Brianna Grado-WhiteDon Marolf
Marija Tomašević

and work in progress w/
Marija Tomašević

Wormholes in this talkLorentzian

Traversable
In a single universe

What can spacetime do?
What topologies?

What connectivity in space and in time?
Classical or quantum matter?

What does it mean?

Geometric duals of quantum teleportation

Patterns of holographic entanglement

Are they possible?

Negative null energy requiredfocusing

defocusing

Repulsive effect on light rays𝜇 𝜈𝑇ℓℓ <0𝜇𝜈
Negative null energy

Topological censorship
Assume Null Energy Condition (NEC)𝑇𝜇𝜈 ℓ𝜇 ℓ𝜈 ≥ 0Then, causal curves are deformableto boundary of spacetime⇒ ∄wormholes
Galloway+Schleich+Witt+Woolgar

Weaker assumption
Averaged (integrated) Null Energy Condition (ANEC)න 𝑑𝜆 𝑇𝜇𝜈 ℓ𝜇 ℓ𝜈 ≥ 0𝛾

is enough for theorem

𝛾: complete null curveEven weaker assumption

Graham+Olum 2007

Achronal Averaged Null Energy Condition (AANEC)𝜇 𝜈𝑑𝜆𝑇ℓℓ ≥ 0 along achronal null lines‫𝛾׬‬𝜇𝜈
“chronal”

achronal light ray = “fastest path”

timelikefasterClassical MatterNull Energy is positive (NEC)Cannot defocus
Traversable wormholes impossible

Quantum Matter
Null Energy can be negative NEC⇒ traversable wormholes become possible

Achronal ANEC holds⇒ only long wormholes

GSL⇒AANEC Wall 2009

Quantum Physics
Null Energy can be negative NEC⇒ traversable wormholes become possible

Achronal ANEC holds⇒ only long wormholes

ANEC in Casimir cylinder
Casimir energy <0න 𝑑𝜆 𝑇𝜇𝜈 ℓ𝜇 ℓ𝜈 < 0𝛾

but this null geodesic is not achronal

Achronal ANEC holds

Quantum Physics
Achronal ANEC implies:• Short wormholes impossible• Inter-universe wormholes impossible• Long wormholes possible

Long wormhole

Achronal ANEC 

integrated energy > 0achronal

integrated energy < 0but not fastest path“chronal”

Short wormhole

integrated energy < 0fastest pathachronal

Achronal ANEC inter-universe wormhole: ultra-shortNeed• long throats• quantum -ve energy to overcome+ve classical energy

Near-extremal Reissner-Nordstrom• long throat• large redshift: small energies

Maldacena+Milekhin+Popov 2018

Near-extremal RN
near horizon

AdS2 x S2non-traversable
wormhole

traversable
wormhole

ER bridge

Rindler-AdS2
2𝑑𝑟𝑑𝑠 2 = − 𝑟 2 − 1 𝑑𝑡 2 + 2
𝑟 −1

Global AdS22𝑑𝑟𝑑𝑠 2 = − 𝑟 2 + 1 𝑑𝑡 2 + 2𝑟 +1

non-traversable
wormhole

traversable
wormhole

ER bridge

Rindler-AdS2
2𝑑𝑟
𝑑𝑠 2 = − 𝑟 2 − 1 𝑑𝑡 2 + 2
𝑟 −1

positive energy above
extremality

Global AdS2
2𝑑𝑟
𝑑𝑠 2 = − 𝑟 2 + 1 𝑑𝑡 2 + 2
𝑟 +1

negative energy

M>Q Reissner-Nordstrom

if lower energy is required,then, how about M<Q?
shrinks
horizonM>Q Reissner-Nordstrom

shrinks
horizonM<Q Reissner-Nordstrom“flares out”

but singularclassical negativeenergy

Perturb M>Q Reissner-Nordstrom w/

negative-energy quantum matter
ER bridge (“almost traversable” wormhole)⟶ traversable wormhole

Need Quantum
Negative Casimir energy
Where/how?
𝑆1

𝑆1 × 𝑆 2 − {∞}Casimir in 𝑆 2 won’t doCasimir in 𝑆1 does it
𝑆2

Negative Casimir energy from massless (conformal)

effective 1+1 fields along 𝑆
𝑆11Electrons in magnetic RN
Landau ground state level
Maldacena+Milekhin+Popov 2018

“Dark CFT” from 5D bulk
Maldacena+Milekhin 2020

Energetics𝑑≪ℓ−𝑄

𝑁𝑓 “electrons”

𝑄ℓEnergy “above” extremality
𝜋 3/2 𝑄 3 𝑙𝑃 𝑁𝑓 𝑄
𝐸=−
2ℓ
8ℓ
Classical, from RN
redshift → small

Quantum
Casimir in 𝑆1

Energetics−𝑄𝑄

Energy “above” extremality
𝑁𝑓 𝑄
𝐸𝑏𝑖𝑛𝑑𝑖𝑛𝑔 = −16ℓ

𝑁𝑓 “electrons”

ℓ

𝑑−𝑄

𝑄Remarks• Small binding energy: fragile wormhole

𝑁𝑓 “electrons”ℓ• May allow for 𝑑 < ℓ∼• Can only make single-universe wormholes• Attraction between mouths?
𝑁𝑓 𝑄
𝐸𝑏𝑖𝑛𝑑𝑖𝑛𝑔 = −16ℓ• merger time 𝑑 3/2 long enough to cross• may balance w/ fluxtube, strings, rotation…

Variations on the theme of wormholes
More versatile constructions:• Casimir energy from cosmic string zero-modes
on 𝑆1

Fu+Grado-White+Marolf 2018

• Several 𝑈 1 s

Entanglement and Teleportation
Gao+Jafferis+Wall 2016
Maldacena+Qi 2018

The two “black hole mouths” are entangled

Microscopic degrees of freedom in Bell-like state
Sending a particle through a wormhole is dual to using
entanglement as resource for quantum teleportation

Multiple wormholes?

Fragile!

Make small corrections

Three-mouth wormholes
Acquire a ready-made wormhole
Insert a small black hole in it

Connect to small black hole outside

Inserting the small mouthTechnically straightforward:
Perturbations w/ matched asymptotics

How large the third black hole?
Choking the throat?

Semiclassical black holes have 𝑚 ≫ 𝑚𝑃𝑙𝑎𝑛𝑐𝑘
Throat redshift helps, but how large can 𝑚 be?

Backreaction calculation shows that throat remains open if
1small bh mass 𝑚 <𝑁𝑓 𝑚𝑃𝑙𝑎𝑛𝑐𝑘
8 𝜋

Then 𝐸𝑏ℎ < |𝐸𝑏𝑖𝑛𝑑𝑖𝑛𝑔 |⇒ if 𝑁𝑓 ≫ 1 then a semiclassical three-mouth wormhole
is possible(also need small enough bh radius to fit inside throat – can do it)Lowering the mass
Choking the throat, now?

Near the big mouth𝑚 ≫ |𝐸𝑏𝑖𝑛𝑑𝑖𝑛𝑔 |(no redshift help)

Lowering the mass
Lower it à la Geroch
Slowly, hanging from a string
Calculation shows it is safe for
1𝑚<𝑁𝑓 𝑚𝑃𝑙𝑎𝑛𝑐𝑘
∼8 𝜋

So
It is possible to construct three-mouth wormholes

with two big mouths/one small mouthSmallsmouth strikes again

Can insert many small mouths
as long as σ𝑖 𝐸𝑏ℎ,𝑖 < |𝐸𝑏𝑖𝑛𝑑𝑖𝑛𝑔 |Signalling between mouths
ABc

Leaky pipeline
Particle or wave from A to B may be(partially) absorbed by cAbsorption ∝ area of c ∝ dof’s of c
Angular dependence ↔ 𝑆𝑈(2) R-charge ofqubitsSignalling between mouths
ABc

Time delay

Message from A to B delayed (Shapiro)
by mass c
Increased complexity of decoding themessage

Multi-partite entanglement
Marolf+Maxfield+Peach+Ross 2015

Mostly bipartite entanglement

Tripartite entanglement

Multi-partite entanglement

Mostly bipartite entanglement

Tripartite entanglement

Conclusions• Intra-universe traversable wormholes areMaldacena+Milekhin+Popovphysically allowed
Fu+Grado-White+Marolf• Multi-mouth traversable wormholes also
allowed – two big mouths + small mouths• Multi-wormholes reveal new multi-partite
holographic entanglement structures