Sean A. Hartnoll, Gary T. Horowitz, Jorrit Kruthoff, Jorge E. Santos
SciPost Phys. 10, 009 (2021) ·
published 15 January 2021
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Charged black holes in anti-de Sitter space become unstable to forming
charged scalar hair at low temperatures $T < T_\text{c}$. This phenomenon is a
holographic realization of superconductivity. We look inside the horizon of
these holographic superconductors and find intricate dynamical behavior. The
spacetime ends at a spacelike Kasner singularity, and there is no Cauchy
horizon. Before reaching the singularity, there are several intermediate
regimes which we study both analytically and numerically. These include strong
Josephson oscillations in the condensate and possible 'Kasner inversions' in
which after many e-folds of expansion, the Einstein-Rosen bridge contracts
towards the singularity. Due to the Josephson oscillations, the number of
Kasner inversions depends very sensitively on $T$, and diverges at a discrete
set of temperatures $\{T_n\}$ that accumulate at $T_c$. Near these $T_n$, the
final Kasner exponent exhibits fractal-like behavior.
SciPost Phys. 9, 001 (2020) ·
published 1 July 2020
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It has been suggested in recent work that the Page curve of Hawking radiation
can be recovered using computations in semi-classical gravity provided one
allows for "islands" in the gravity region of quantum systems coupled to
gravity. The explicit computations so far have been restricted to black holes
in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically
construct a five-dimensional asymptotically AdS geometry whose boundary
realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole
in equilibrium with a bath. We also numerically find two types of extremal
surfaces: ones that correspond to having or not having an island. The version
of the information paradox involving the eternal black hole exists in this
setup, and it is avoided by the presence of islands. Thus, recent computations
exhibiting islands in two-dimensional gravity generalize to higher dimensions
as well.
