Built on

A. Larkin and Y. Ovchinnikov, “Quasiclassical method in the theory of superconductivity,” JETP 28
1969
Earlier work this paper cites.
S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse,” Phys. Rev. D 14
1976
Earlier work this paper cites.
T. Dray and G. ’t Hooft, “The Gravitational Shock Wave of a Massless Particle,” Nucl. Phys. B 253
1985
Earlier work this paper cites.
G. ’t Hooft, “The black hole interpretation of string theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
D. N. Page, “Information in black hole radiation,” Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
Y. Kiem, H. L. Verlinde and E. P. Verlinde, “Black hole horizons and complementarity,” Phys. Rev. D 52
1995
Earlier work this paper cites.
R. Bousso, “Complementarity Is Not Enough,” Phys. Rev. D 87
Original
1995
Earlier work this paper cites.
G. ’t Hooft, “The Scattering matrix approach for the quantum black hole: An Overview,” Int. J. Mod. Phys. A 11
1996
Earlier work this paper cites.

Similar

G. Festuccia and H. Liu, “The Arrow of time, black holes, and quantum mixing of large N Yang-Mills theories,” JHEP 0712
2007
Cited alongside, same era.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Cited alongside, same era.
N. Iizuka and J. Polchinski, “A Matrix Model for Black Hole Thermalization,” JHEP 0810
Original
2008
Cited alongside, same era.
S. D. Mathur, “The Information paradox: A Pedagogical introduction,” Class. Quant. Grav. 26
Original
2009
Cited alongside, same era.
N. Iizuka, T. Okuda and J. Polchinski, “Matrix Models for the Black Hole Information Paradox,” JHEP 1002
Original

Then

L. Susskind, “The Transfer of Entanglement: The Case for Firewalls,” arXiv:1210.2098 [hep-th]; K. Papadodimas and S. Raju, “An Infalling Observer in AdS/CFT,” JHEP 1310
Original
2013
Later among the works it cites.
S. B. Giddings, “Nonviolent nonlocality,” Phys. Rev. D 88
Original
2013
Later among the works it cites.
S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,” JHEP 1403
Original
2014
Later among the works it cites.
S. H. Shenker and D. Stanford, “Multiple Shocks,” JHEP 1412
Original
2014
Later among the works it cites.
S. Leichenauer, “Disrupting Entanglement of Black Holes,” Phys. Rev. D 90
Original

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2015

Chaos in the black hole S-matrix

Polchinski, Joseph

Understand

Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior.

We extend this from eternal black holes to black holes that form and then evaporate.
This leads to an identity for the change in the black hole S-matrix (over times shorter than the scrambling time) due an addition infalling particle, elaborating an idea of 't Hooft.

Built on

A. Larkin and Y. Ovchinnikov, “Quasiclassical method in the theory of superconductivity,” JETP 28
1969
Earlier work this paper cites.
S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse,” Phys. Rev. D 14
1976
Earlier work this paper cites.
T. Dray and G. ’t Hooft, “The Gravitational Shock Wave of a Massless Particle,” Nucl. Phys. B 253
1985
Earlier work this paper cites.
G. ’t Hooft, “The black hole interpretation of string theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
D. N. Page, “Information in black hole radiation,” Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
Y. Kiem, H. L. Verlinde and E. P. Verlinde, “Black hole horizons and complementarity,” Phys. Rev. D 52
1995
Earlier work this paper cites.
R. Bousso, “Complementarity Is Not Enough,” Phys. Rev. D 87
Original
1995
Earlier work this paper cites.
G. ’t Hooft, “The Scattering matrix approach for the quantum black hole: An Overview,” Int. J. Mod. Phys. A 11
1996
Earlier work this paper cites.

Similar

G. Festuccia and H. Liu, “The Arrow of time, black holes, and quantum mixing of large N Yang-Mills theories,” JHEP 0712
2007
Cited alongside, same era.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Cited alongside, same era.
N. Iizuka and J. Polchinski, “A Matrix Model for Black Hole Thermalization,” JHEP 0810
Original
2008
Cited alongside, same era.
S. D. Mathur, “The Information paradox: A Pedagogical introduction,” Class. Quant. Grav. 26
Original
2009
Cited alongside, same era.
N. Iizuka, T. Okuda and J. Polchinski, “Matrix Models for the Black Hole Information Paradox,” JHEP 1002
Original

Then

L. Susskind, “The Transfer of Entanglement: The Case for Firewalls,” arXiv:1210.2098 [hep-th]; K. Papadodimas and S. Raju, “An Infalling Observer in AdS/CFT,” JHEP 1310
Original
2013
Later among the works it cites.
S. B. Giddings, “Nonviolent nonlocality,” Phys. Rev. D 88
Original
2013
Later among the works it cites.
S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,” JHEP 1403
Original
2014
Later among the works it cites.
S. H. Shenker and D. Stanford, “Multiple Shocks,” JHEP 1412
Original
2014
Later among the works it cites.
S. Leichenauer, “Disrupting Entanglement of Black Holes,” Phys. Rev. D 90
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2010

Cited alongside, same era.

S. G. Avery, B. D. Chowdhury and A. Puhm, “Unitarity and fuzzball complementarity: ‘Alice fuzzes but may not even know it!’,” JHEP 1309

Original

2013

Cited alongside, same era.

A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 1302

Original

2013

Cited alongside, same era.

S. H. Shenker and D. Stanford, “Stringy effects in scrambling,” arXiv:1412.6087 [hep-th]

Original

Cited in the paper.

S. Jackson, L. McGough and H. Verlinde, “Conformal Bootstrap, Universality and Gravitational Scattering,” arXiv:1412.5205 [hep-th]

Original

Cited in the paper.

J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos,” arXiv:1503.01409 [hep-th]

Original

Cited in the paper.

N. Itzhaki, “Some remarks on ’t Hooft’s S matrix for black holes,” hep-th/9603067; N. Itzhaki, “Is the black hole complementarity principle really necessary?,” hep-th/9607028

Cited in the paper.

M. Dodelson and E. Silverstein, “String-theoretic breakdown of effective field theory near black hole horizons,” arXiv:1504.05536 [hep-th]; M. Dodelson and E. Silverstein, “Longitudinal nonlocality in the string S-matrix,” arXiv:1504.05537 [hep-th]

Original

Cited in the paper.

2014

Later among the works it cites.

R. Akhoury, “Unitary S Matrices With Long-Range Correlations and the Quantum Black Hole,” JHEP 1408

Original

2014

Later among the works it cites.

A. Kitaev, “Hidden correlations in the Hawking radiation and thermal noise,” Breakthrough Prize Fundamental Physics Symposium 11/10/2014, KITP seminar 2/12/2015; “A simple model of quantum holography (part 1),” KITP seminar 4/7/2015

2015

Closest in time.