Restricted Maximin surfaces and HRT in generic black hole spacetimes
- PDF / 248,140 Bytes
- 9 Pages / 595.276 x 841.89 pts (A4) Page_size
- 14 Downloads / 161 Views
Springer
Received: May 4, 2019 Accepted: May 13, 2019 Published: May 22, 2019
Donald Marolf,a Aron C. Wallb and Zhencheng Wanga a
Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A. b Stanford Institute for Theoretical Physics, Stanford University, 382 Via Pueblo, Stanford, CA 94305, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: The AdS/CFT understanding of CFT entanglement is based on HRT surfaces in the dual bulk spacetime. While such surfaces need not exist in sufficiently general spacetimes, the maximin construction demonstrates that they can be found in any smooth asymptotically locally AdS spacetime without horizons or with only Kasner-like singularities. In this work, we introduce restricted maximin surfaces anchored to a particular boundary Cauchy slice C∂ . We show that the result agrees with the original unrestricted maximin prescription when the restricted maximin surface lies in a smooth region of spacetime. We then use this construction to extend the existence theorem for HRT surfaces to generic charged or spinning AdS black holes whose mass-inflation singularities are not Kasner-like. We also discuss related issues in time-independent charged wormholes. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Black Holes ArXiv ePrint: 1901.03879
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)127
JHEP05(2019)127
Restricted Maximin surfaces and HRT in generic black hole spacetimes
Contents 1
2 Restricted maximin surfaces 2.1 Equivalence of HRT surfaces and restricted maximin surfaces in smooth regions of spacetime 2.2 Existence of HRT surfaces in standard charged and rotating black holes
3
3 Discussion
6
1
4 5
Introduction
As is by now well established [1, 2], in AdS/CFT the Ryu-Takayangi [3, 4] and HubenyRangamani-Takayanagi (HRT) [5] prescriptions generally describe the von Neumann entropy of CFT regions A in terms of the area of an appropriate bulk surface. In particular, SA =
Area[ext(A)] , 4G
(1.1)
where ext(A) is the smallest extremal surface satisfying ∂(ext(A)) = ∂A and with ext(A) homologous to A. When there is more than one such surface with minimal area, the HRT surface is ambiguous. Such situations arise at HRT phase transitions, when the HRT surface jumps discontinuously as one varies the region A. Now, there are spacetimes in which HRT surfaces fail to exist or where those that do exist do not correctly compute the von Neumann entropy [6]. However, known spacetimes M0 with the latter issue are λ → 0 limits of spacetimes Mλ in which the HRT prescription succeeds, but where the correct (smallest) extremal surface recedes to the future or past singularity as λ → 0. Similarly, known spacetimes M00 where extremal surfaces fail to exist are again λ → 0 limits of spacetimes Mλ where HRT succeeds but in which all extremal surfaces recede in this way. One thus expects that HRT surfaces do in fact correctly compute the entropy in contexts such reces
Data Loading...
