Horizontal Charge Excitation ofSupertranslation and Superrotation
Masahiro Hotta

Tohoku University
Based onM. Hotta, J. Trevison and K. Yamaguchi arXiv:1606.02443.
M. Hotta, K. Sasaki and T. Sasaki, Class. Quantum Grav. 18, 1823 (2001).
M. Hotta, Phys. Rev. D 66, 124021 (2002).

Jose Trevison

Koji Yamaguchi

Introduction
Two Big Problems in Black Hole Physics○ Black Hole Information Loss Problem
Is the process of black hole formation and evaporation unitary?

○ Black Hole Entropy Problem
What is the spacetime origin of statistical mechanical black holeentropy A /(4G ) ? Where do the quantum states live in the spacetime?

Hawking, Perry and Strominger (HPS) proposed asymmetry-based conjecture of simultaneous resolutionof the information loss problem and the black holeentropy problem, using supertranslation andsuperrotation on a black hole horizon, and BMS
gravitational degeneracy of vacuum states at the null
future infinity.
S. W. Hawking, "The Information Paradox for Black Holes", arXiv:1509.01147.
S. W. Hawking, M. J. Perry and A. Strominger, "Soft Hair on Black Holes", arXiv:1601.00921.

+δx= T (θ , φ ) + ←Supertranslation
Near-Horizon Asymptotic Metric of HPSAA←SuperrotationxRδθ
φ=(,)++2AB
ds = 2dx dr + g dx dx + O(r − r )∑θφABH,Horizon

HorizonCollapsing
MatterHorizon(θ , φ )⊗ Area /( 4 G )Soft hair of BH

ln Wsoft hair ≈ Area /(4G )r = rHµ∂ µ J (i ) = 0x−

Collapsing
Matterx+
An infinite number of holographic charges
on the horizon store whole quantum
information of absorbed matter.
Unitarity

HPS said,“Stationary black holes do not carry classicalsupertranslation hair.” (arXiv:1601.00921)
So they consider purely quantum supertranslation
hair on the horizon with reluctance.

r = rHQ[ξ ] = 0

HPS coordinate system near horizon is
physically implemented by free-falling blocknumbered clocks distributed in the space.

ds = 2dx dr + ∑ g AB dx dx + O(r − rH )2Horizonx++AB

θ ,φFree fall motion of the clocks makes
HPS classical supertranslation charge vanishon the horizon due to the equivalence principle.

ρ =∞Q[ξ ] ≠ 0Horizonv~MASSAGE (I) of THIS TALK~In a Rindler-type coordinate system
implemented by accelerating blocknumbered clocks distributed in the space,stationary black holes indeed carrynon-vanishing classical charges ofsupertranslation and superrotation.
【M. Hotta, K. Sasaki and T. Sasaki,
Class. Quantum Grav. 18, 1823 (2001) 】
Similarity to Unruh effect.

ds = 2 exp(− ρ / κ )dvdρ + ∑ g AB dx dx + A

2Rindler factor

θ ,φB(κ = 16πG )~MASSAGE (II) of THIS TALK~Taking a large blackhole mass limit, near-horizon geometry of a black hole isdescribed by Minkowski space, and the horizon is mapped into one of Rindler
horizons.
【M. Hotta, J. Trevison and K. Yamaguchi arXiv:1606.02443 】

We construct a general theory of gravitational holographic
charges on Rindler horizons for a 1+3 dimensional linearized
gravity field in the Minkowski background. Especially, wegive a general formula of holographic charge shift ofsupertranslation and superrotation induced by infalling
matter absorption. Gravitational wave absorption cannot
make transition between different charged states.

~MASSAGE (III) of THIS TALK~
By using quantum gravitational memory charges,
we claim that the holographic pixel on every Rindler
horizon is an emergent concept, which is subjective toquantum measurement contexuality. The no-cloning
paradox of quantum information between matter insideof the horizon and holographic charges on the horizon
may not arise.
【M. Hotta, J. Trevison and K. Yamaguchi arXiv:1606.02443 】

Accelerating clocks
as a metric detector
observe BH soft hairin this room, as well
as Hawking-Unruh
thermal bath!

Q[ξ ] ≠ 0

Non-ontological holographic screen

Main Results【M. Hotta, J. Trevison and K. Yamaguchi arXiv:1606.02443 】

RindlerHorizont

Infalling matterx = 0 (ρ = ∞ )−Q[ξ ] ≠ 0T+ + ρ τ x = 2κ exp − 2κ hµν±x

Minkowski
spacetime[]ds = 2 exp(− ρ / κ ) − dτ + dρ + dy + dz Rindler metric background22222

Asymptotic symmetry near a horizon:yzτδ ξτ = ξ ( y, z ), δ ξ ρ = 0, δ ξ y = ξ ( y, z ), δ ξ z = ξ ( y, z ).
Supertranslation Charge on Horizon

[ ]()

∞
1
τ++−+
Qst ξ = −dydzξ ( y, z ) ∫ x T+ + x , x = 0, y, z dx
∫02κτ(Superrotation Charge on Horizon κ = 16πG[Qsr ξ , ξyz])

 ( y − y ') + ( z − z ') 
1A()=∂'',lnξdydz
dydzyz
A2
∫
∫
4πκ

2

∞()

× ∫ ∂ −T+ + x , x = 0, y ' , z ' dx
0+−+2

Cf: ’t Hooft’s blackhole S matrix

T+ + = 0 ⇒ Q[ξ ] = 0Weak gravitational waves cannot make transitions between
physical states with different charges. Horizon as aholographic screen does not store the information at all.

⇒ doubt of HPS resolution of the information loss problem.
→ The result is still consistent with the scenario of zero-point
fluctuation partner of Hawking particle
for a resolution of the information loss problem.
(Wilczek 1992, Hotta-Schüzhold-Unruh 2015, Hotta-Sugita 2015)

About the No-Cloning Paradox

No-cloning paradox between two
quantum gravitational memories

Q̂' [ξ ]Q̂[ξ ]Singularity

Holographic charge stores
quantum information of thecollapsing matter.

New holographic charge
stores quantum informationof the collapsing matter +additional infalling matter.

Newhorizon

Oldhorizon

Collapsing
matterAdditional
infalling
matterAdditional
infallingmatter

In HPS, new holographic charge has tostore whole the quantum informationof the collapsing matter before theadditional matter comes in!
Duplicate quantum information on
two different horizons.
No-cloning paradox
between two gravitational
memories even in large BH mass limit?

Q̂[ξ ]

Newhorizon

Q̂' [ξ ]x − = xh

Resolution: NoncommutativeGravitational Memory Charges on
Different Rindler Horizons[(()+h−hTˆ+ +() ()∞1+ ˆ−++++
τdydzξ ( y, z )∫ x + xh T+ + x + x h , xh , y, z dx
=−
∫02κ
22


()
()
1''yyzz−+−
Adydz ∫ dy ' dz 'ξ ( y, z )∂ A ln +2
∫
4πκ


∞

()−++
ˆ× ∫ ∂ −T+ + x + x h , xh , y ' , z ' dx +0)(x , x )+−+−ˆˆQ xh , xh , Q x ' h , x ' h ≠ 0+−ˆ
Q xh , xh(+−ˆQ xh , xh)]) (−Q̂old horizon[QˆtQ̂new horizon]

ˆ,Q≠0old horizon
new horizon

Two gravitational memories areobservables dependent on each other!
Measurement of one of the memories
deletes quantum information in theother memory via wave function
collapse.

x

How about no-cloning paradox
between absorbed matter andquantum gravitational memory?

No decoherencetΨ (t )Whole information
about Û is carried bythe matter.

xInfallingmatterΨ = Û 0Information

t

Rindler
HorizonQ̂[ξ ] ⇒ Quantum

information
about Ûx
InfallingmatterΨ = Û 0

Decoherence
happens?

tRindler
HorizonQ̂[ξ ] ⇒ Quantum

information
about Ûx
InfallingmatterΨ = Û 0

Resolution:
In order to measure the information stored in theholographic charges, metric detectors are required.
However, the detectors inevitably interact with
the infalling matter and share quantum
entanglement.
This causes decoherence of the infalling matter,and no exact duplicate quantum information
exists. This evades the no-cloning paradox.

Q̂[ξ ]
y = 1, z = 1

RindlerHorizon

y = 0, z = 1−x =0z

Signalexchange
betweenclocks

Weak gravity fieldĥµν

y = 1, z = 0
y = 0, z = 0y

Accelerating metric detectors distributed
slightly outside of the horizonˆT+ +Decoheredinfalling matter

Gravitational interaction generates
entanglement between the matterand the detector. This indeed causes
decoherence. If no detectors,
no decoherence happens.

tEntanglement

Metric detector
for measurement of Q̂ ξ[]xΨ = Û 0

【Status Summary of HPS Scenario】○ Black Hole Entropy Problem →(Hotta 2002, Hawking-Perry-Strominger 2016, Hotta-Trevison-Yamaguchi 2016)○ Black Hole Information Loss Problem →(Hotta-Trevison-Yamaguchi 2016)

Soft hair on horizon may be so thick that the black hole entropy
problem is resolved, but too thin to resolve the information loss
problem.
For the resolution of information loss,
the scenario of zero-point fluctuation partner of Hawking particle
remains fascinating. Wilczek 1992 Hotta-Schüzhold-Unruh 2015 Hotta-Sugita 2015

Summary○ In a Rindler coordinate system implemented by accelerating blocknumbered clocks distributed in the space, stationary black holes indeed carrynon-vanishing classical charges of supertranslation and superrotation.
Similarity to Unruh effect.
○ General theory of gravitational holographic charges on Rindler horizons for a
1+3 dimensional linearized gravity field in the Minkowski background.
General formula of holographic charge shift of supertranslation andsuperrotation induced by infalling matter absorption.
No information of gravitational waves are stored in the leading order.
○ Holographic pixel is an emergent concept, which is subjective to quantum
measurement contexuality. The no-cloning paradox of quantum information
between matter inside of the horizon and holographic charges on thehorizon may not arise.