Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
- PDF / 2,700,584 Bytes
- 24 Pages / 595.276 x 841.89 pts (A4) Page_size
- 90 Downloads / 204 Views
Springer
Received: July 31, Revised: September 7, Accepted: September 17, Published: October 15,
2020 2020 2020 2020
Sean A. Hartnoll,a Gary T. Horowitz,b Jorrit Kruthoffa and Jorge E. Santosc,d a
Department of Physics, Stanford University, Stanford, CA 94305-4060, U.S.A. b Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A. c DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, U.K. d Institute for Advanced Study, Princeton, NJ 08540, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes — for example ReissnerNordstr¨om-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. Keywords: Black Holes, Spacetime Singularities, AdS-CFT Correspondence, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 2006.10056
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)102
JHEP10(2020)102
Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
Contents 1
2 Background and equations
4
3 Horizons 3.1 Relevant deformations remove Cauchy horizons 3.2 Irrelevant deformations can have fine-tuned Cauchy horizons
5 6 6
4 Collapse of the Einstein-Rosen bridge
9
5 Kasner singularity
10
6 Penrose diagrams
13
7 Dilatonic theories: Lifshitz to Kasner
14
8 Traversing geodesics
17
9 Discussion
18
1
Introduction
Black hole interiors present many theoretical challenges, at both a classical and quantum level. One of these challenges is the singularity at which spacetime ends [1]. The classical approach to generic singularities is expected to be very complicated [2], while the classical description itself eventually breaks down as curvatures become large. Another challenge is the possible presence of Cauchy horizons, at which the predictability of the classical dynamics breaks down, even away from regions with large curvature [3]. The strong cosmic censorship conjecture posits that such Cauchy horizons are artifacts of some highly symmetric solutions that are known analytically, and do not arise from generic initial data [4]. In holographic duality, eternal black holes in asymptotically AdS spacetimes arise as th
Data Loading...
