Built on

V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report , Living Rev. Rel. 22
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1904
Earlier work this paper cites.
R. Karlsson, M. Kulaxizi, A. Parnachev and P. Tadić, Black Holes and Conformal Regge Bootstrap , JHEP 10
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1904
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I. Bena, P. Heidmann, R. Monten and N. P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries , SciPost Phys. 7
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Y. Kiem, H. L. Verlinde and E. P. Verlinde, Black hole horizons and complementarity , Phys. Rev. D52
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O. Lunin and S. D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon , Phys. Rev. Lett. 88
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O. Lunin and S. D. Mathur, AdS / CFT duality and the black hole information paradox , Nucl. Phys. B623
2002
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S. D. Mathur, The Fuzzball proposal for black holes: An Elementary review , Fortsch. Phys. 53
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2020

Chaos at the rim of black hole and fuzzball shadows

Bianchi, Massimo, Grillo, Alfredo, Morales, Jose Francisco

Understand

We study the scattering of massless probes in the vicinity of the {\it photon-sphere} of asymptotically AdS black holes and horizon-free microstate geometries (fuzzballs).

We find that these exhibit a chaotic behaviour characterised by exponentially large deviations of nearby trajectories.
We compute the Lyapunov exponent $\lambda$ governing the exponential growth in $d$ dimensions and show that it is bounded from above by $\lambda_b = \sqrt{d{-}3}/2b_{\rm min}$ where $b_{\rm min}$ is the minimal impact parameter under which a massless particle is swallowed by the black hole or gets trapped in the fuzzball for a very long time.
Moreover we observe that $\lambda$ is typically below the advocated bound on chaos $\lambda_H=2\pi \kappa_B T/\hbar$, that in turn characterises the radial fall into the horizon, but the bound is violated in a narrow window near extremality, where the photon-sphere coalesces with the horizon.

Built on

V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report , Living Rev. Rel. 22
Original
1904
Earlier work this paper cites.
R. Karlsson, M. Kulaxizi, A. Parnachev and P. Tadić, Black Holes and Conformal Regge Bootstrap , JHEP 10
Original
1904
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.
S. Hollands, R. M. Wald and J. Zahn, Quantum Instability of the Cauchy Horizon in Reissner-Nordström-deSitter Spacetime , 1912.06047
Original
1912
Earlier work this paper cites.
H. A. Buchdahl, General Relativistic Fluid Spheres , Phys. Rev. 116
1959
Earlier work this paper cites.
S. Chandrasekhar, The mathematical theory of black holes , in Oxford, UK: Clarendon (1992) 646 p., OXFORD, UK: CLARENDON (1985) 646 P. , 1985
1985
Earlier work this paper cites.
Y. Kiem, H. L. Verlinde and E. P. Verlinde, Black hole horizons and complementarity , Phys. Rev. D52
1995
Earlier work this paper cites.
M. M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories , Class. Quant. Grav. 17
2000
Earlier work this paper cites.
O. Lunin and S. D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon , Phys. Rev. Lett. 88
2002
Earlier work this paper cites.
O. Lunin and S. D. Mathur, AdS / CFT duality and the black hole information paradox , Nucl. Phys. B623
2002
Earlier work this paper cites.
S. D. Mathur, The Fuzzball proposal for black holes: An Elementary review , Fortsch. Phys. 53
2005
Earlier work this paper cites.