A Dynamical Boundary for Anti-de Sitter Space
Abstract
We argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the {\em renormalized} boundary stress tensor density fixed, instead of the boundary metric. This leads to a well-defined variational problem, as well as new counter-terms and a finite on-shell action. We elaborate this in various (even and odd) dimensions in the language of holographic renormalization. Even though the {\em form} of the new renormalized action is distinct from the standard one, once the cut-off is taken to infinity, their {\em values} on classical solutions coincide when the trace anomaly vanishes. For AdS, we compute the ADM form of this renormalized action and show in detail how the correct thermodynamics of Kerr-AdS black holes emerge. We comment on the possibility of a consistent quantization with our boundary conditions when the boundary is dynamical, and make a connection to the results of Compere and Marolf. The difference between our approach and microcanonical-like ensembles in standard AdS/CFT is emphasized.
Keywords
Cite
@article{arxiv.1609.06300,
title = {A Dynamical Boundary for Anti-de Sitter Space},
author = {Chethan Krishnan and Avinash Raju and P. N. Bala Subramanian},
journal= {arXiv preprint arXiv:1609.06300},
year = {2016}
}
Comments
v2: more remarks, many more references, 33 pp, PRD version