Built on

V. Jahnke, K.-Y. Kim and J. Yoon, On the Chaos Bound in Rotating Black Holes , JHEP 05
Original
1903
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox , JHEP 09
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole , JHEP 12
Original
1905
Earlier work this paper cites.
I. Bena, P. Heidmann, R. Monten and N. P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries , SciPost Phys. 7
Original
1905
Earlier work this paper cites.
M. Mezei and G. Sárosi, Chaos in the butterfly cone , JHEP 01
Original
1908
Earlier work this paper cites.
I. Halder, Global Symmetry and Maximal Chaos , 1908.05281
Original
1908
Earlier work this paper cites.
V. Balasubramanian, B. Craps, M. De Clerck and K. Nguyen, Superluminal chaos after a quantum quench , JHEP 12
Original
1908
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior , 1911.11977
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , JHEP 05
Original
1911
Earlier work this paper cites.
S. E. Gralla, A. Ravishankar and P. Zimmerman, Horizon Instability of the Extremal BTZ Black Hole , JHEP 05
Original
1911
Earlier work this paper cites.
A. Banerjee, A. Kundu and R. R. Poojary, Rotating Black Holes in AdS, Extremality and Chaos , 1912.12996
Original
1912
Earlier work this paper cites.
J. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity , Commun. Math. Phys. 104
1986
Earlier work this paper cites.
N. Cruz, C. Martinez and L. Pena, Geodesic structure of the (2+1) black hole , Class. Quant. Grav. 11
1994
Earlier work this paper cites.
K. Sfetsos, On gravitational shock waves in curved space-times , Nucl. Phys. B 436
1995
Earlier work this paper cites.
S. Carlip, The (2+1)-Dimensional black hole , Class. Quant. Grav. 12
1995
Earlier work this paper cites.

Similar

M. Bianchi, A. Grillo and J. F. Morales, Chaos at the rim of black hole and fuzzball shadows , JHEP 05
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2002
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D. Birmingham, I. Sachs and S. N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes , Phys. Rev. Lett. 88
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J. M. Maldacena, Eternal black holes in anti-de Sitter , JHEP 04
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Cited alongside, same era.
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Original
2006
Cited alongside, same era.

Then

S. H. Shenker and D. Stanford, Stringy effects in scrambling , JHEP 05
Original
2015
Later among the works it cites.
D. A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect , Phys. Rev. Lett. 115
Original
2015
Later among the works it cites.
I. Bena, S. Giusto, E. J. Martinec, R. Russo, M. Shigemori, D. Turton et al., Smooth horizonless geometries deep inside the black-hole regime , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
J. Maldacena, S. H. Shenker and D. Stanford, A bound on chaos , JHEP 08
Original
2016
Later among the works it cites.
A. L. Fitzpatrick and J. Kaplan, Conformal Blocks Beyond the Semi-Classical Limit , JHEP 05

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2020

Slow scrambling in extremal BTZ and microstate geometries

Craps, Ben, De Clerck, Marine, Hacker, Philip et al.

Understand

Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon.

This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries.
This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes.
In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display "slow scrambling", characterized by cubic (rather than exponential) growth.

Built on

V. Jahnke, K.-Y. Kim and J. Yoon, On the Chaos Bound in Rotating Black Holes , JHEP 05
Original
1903
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox , JHEP 09
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole , JHEP 12
Original
1905
Earlier work this paper cites.
I. Bena, P. Heidmann, R. Monten and N. P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries , SciPost Phys. 7
Original
1905
Earlier work this paper cites.
M. Mezei and G. Sárosi, Chaos in the butterfly cone , JHEP 01
Original
1908
Earlier work this paper cites.
I. Halder, Global Symmetry and Maximal Chaos , 1908.05281
Original
1908
Earlier work this paper cites.
V. Balasubramanian, B. Craps, M. De Clerck and K. Nguyen, Superluminal chaos after a quantum quench , JHEP 12
Original
1908
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior , 1911.11977
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , JHEP 05
Original
1911
Earlier work this paper cites.
S. E. Gralla, A. Ravishankar and P. Zimmerman, Horizon Instability of the Extremal BTZ Black Hole , JHEP 05
Original
1911
Earlier work this paper cites.
A. Banerjee, A. Kundu and R. R. Poojary, Rotating Black Holes in AdS, Extremality and Chaos , 1912.12996
Original
1912
Earlier work this paper cites.
J. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity , Commun. Math. Phys. 104
1986
Earlier work this paper cites.
N. Cruz, C. Martinez and L. Pena, Geodesic structure of the (2+1) black hole , Class. Quant. Grav. 11
1994
Earlier work this paper cites.
K. Sfetsos, On gravitational shock waves in curved space-times , Nucl. Phys. B 436
1995
Earlier work this paper cites.
S. Carlip, The (2+1)-Dimensional black hole , Class. Quant. Grav. 12
1995
Earlier work this paper cites.

Similar

M. Bianchi, A. Grillo and J. F. Morales, Chaos at the rim of black hole and fuzzball shadows , JHEP 05
Original
2002
Cited alongside, same era.
D. Birmingham, I. Sachs and S. N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes , Phys. Rev. Lett. 88
2002
Cited alongside, same era.
J. M. Maldacena, Eternal black holes in anti-de Sitter , JHEP 04
2003
Cited alongside, same era.
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The Library of Babel: On the origin of gravitational thermodynamics , JHEP 12
2005
Cited alongside, same era.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation , 2006.06872
Original
2006
Cited alongside, same era.

Then

S. H. Shenker and D. Stanford, Stringy effects in scrambling , JHEP 05
Original
2015
Later among the works it cites.
D. A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect , Phys. Rev. Lett. 115
Original
2015
Later among the works it cites.
I. Bena, S. Giusto, E. J. Martinec, R. Russo, M. Shigemori, D. Turton et al., Smooth horizonless geometries deep inside the black-hole regime , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
J. Maldacena, S. H. Shenker and D. Stanford, A bound on chaos , JHEP 08
Original
2016
Later among the works it cites.
A. L. Fitzpatrick and J. Kaplan, Conformal Blocks Beyond the Semi-Classical Limit , JHEP 05

Beyond the bibliography

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

Open on alphaXiv

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I. Bena, A. Houppe and N. P. Warner, Delaying the Inevitable: Tidal Disruption in Microstate Geometries , 2006.13939

Original

2006

Cited alongside, same era.

V. Balasubramanian, B. Czech, V. E. Hubeny, K. Larjo, M. Rangamani and J. Simon, Typicality versus thermality: An Analytic distinction , Gen. Rel. Grav. 40

2008

Cited alongside, same era.

B. D. Chowdhury and S. D. Mathur, Radiation from the non-extremal fuzzball , Class. Quant. Grav. 25

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.

V. Cardoso, A. S. Miranda, E. Berti, H. Witek and V. T. Zanchin, Geodesic stability, Lyapunov exponents and quasinormal modes , Phys. Rev. D 79

Original