Abstract
We study the Complexity=Volume conjecture for Warped AdS3 black holes. We compute the spatial volume of the Einstein-Rosen bridge and we find that its growth rate is proportional to the Hawking temperature times the Bekenstein-Hawking entropy. This is consistent with expectations about computational complexity in the boundary theory.
Highlights
Running forward, this geometry is dual to a time-dependent thermofield doublet state [10]
06123 Perugia, Italy cUniversita degli studi di Milano Bicocca and INFN, Sezione di Milano — Bicocca, Piazza della Scienza 3, 20161, Milano, Italy dTIFPA — INFN, c/o Dipartimento di Fisica, Universita di Trento, 38123 Povo (TN), Italy E-mail: roberto.auzzi@unicatt.it, s.baiguera@campus.unimib.it, giuseppe.nardelli@unicatt.it Abstract: We study the Complexity=Volume conjecture for Warped AdS3 black holes
We compute the spatial volume of the Einstein-Rosen bridge and we find that its growth rate is proportional to the Hawking temperature times the Bekenstein-Hawking entropy
Summary
We will be interested in BHs with WAdS3 asymptotic [34, 41, 42]. This class of metrics should be dual to a boundary WCFT at finite temperature. As far as we know, there is no known non-pathological matter content in field theory supporting stretched warped BHs in Einstein gravity [43]. They can be obtained as solutions to a perfect fluid stress tensor with spacelike quadrivelocity [53]. They can arise as a solution of Chern-Simons-Maxwell electrodynamics coupled to Einstein gravity [54, 55], but a wrong sign for the kinetic Maxwell term is required in order to have solutions with no closed time-like curves (which corresponds to ν2 ≥ 1). In the following we take a pragmatical approach: we suppose that a consistent realization of stretched warped BHs in Einstein gravity exists, and we investigate the CV conjecture
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