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A bstract We study the interior of a recently constructed family of asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Inside the horizon, these black holes resemble the interior of a holographic superconductor. There are analogs of the Josephson oscillations of the scalar field, and the final Kasner singularity depends very sensitively on the black hole parameters near the onset of the instability. In an appendix, we give a general argument that Cauchy horizons cannot exist in a large class of stationary black holes with scalar hair.
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Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
A bstract The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes — for example Reissner- Nordström-AdS — can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.
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- Award ID(s):
- 1801805
- PAR ID:
- 10287904
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2020
- Issue:
- 10
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Charged black holes in anti-de Sitter space become unstable to forming charged scalar hair at low temperatures T < Tc. 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 {Tn} that accumulate at Tc. Near these Tn, the final Kasner exponent exhibits fractal-like behavior.more » « less
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Abstract We study the interior of black holes in the presence of charged scalar hair of small amplitude$$\epsilon $$ on the event horizon and show their terminal boundary is a crushing Kasner-like singularity. These spacetimes are spherically symmetric, spatially homogeneous and they differ significantly from the hairy black holes with uncharged matter previously studied in[M. Van de Moortel, Violent nonlinear collapse inside charged hairy black holes, Arch. Rational. Mech. Anal., 248, 89, 2024]in that the electric field is dynamical and subject to the backreaction of charged matter. We prove this charged backreaction causes drastically different dynamics compared to the uncharged case that ultimately impact the formation of the spacelike singularity, exhibiting novel phenomena such asCollapsed oscillations: oscillatory growth of the scalar hair, nonlinearly induced by the collapseAfluctuating collapse: The final Kasner exponents’ dependency in$$\epsilon $$ is via an expression of the form$$|\sin \left( \omega _0 \cdot \epsilon ^{-2}+ O(\log (\epsilon ^{-1}))\right) |$$ .AKasner bounce: a transition from an unstable Kasner metric to a different stable Kasner metricThe Kasner bounce occurring in our spacetime is reminiscent of the celebrated BKL scenario in cosmology. We additionally propose a construction indicating the relevance of the above phenomena – including Kasner bounces – to spacelike singularities inside more general (asymptotically flat) black holes, beyond the hairy case. While our result applies to all values of$$\Lambda \in \mathbb {R}$$ , in the$$\Lambda <0$$ case, our spacetime corresponds to the interior region of a charged asymptotically Anti-de-Sitter stationary black hole, also known as aholographic superconductorin high-energy physics, and whose exterior region was rigorously constructed in the recent mathematical work [W. Zheng,Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes, arXiv.2410.04758].more » « less
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Under the correspondence, asymptotically anti–de Sitter geometries with backreaction can be viewed as conformal field theory states subject to a renormalization group (RG) flow from an ultraviolet (UV) description toward an infrared (IR) sector. For black holes, however, the IR point is the horizon, so one way to interpret the interior is as an analytic continuation to a “trans-IR” imaginary-energy regime. In this paper, we demonstrate that this analytic continuation preserves some imprints of the UV physics, particularly near its “end point” at the classical singularity. We focus on holographic phase transitions of geometric objects in round black holes. We first assert the consistency of interpreting such black holes, including their interiors, as RG flows by constructing a monotonic function. We then explore how UV phase transitions of entanglement entropy and scalar two-point functions, each of which are encoded by bulk geometry under the holographic mapping, are related to the structure of the near-singularity geometry, which is quantified by Kasner exponents. Using 2D holographic flows triggered by relevant scalar deformations as test beds, we find that the 3D bulk’s near-singularity Kasner exponents can be viewed as functions of the UV physics precisely when the deformation is nonzero. Published by the American Physical Society2024more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP10(2020)102
