Comparison between various notions of conserved charges in asymptotically AdS-spacetimes

TL;DR

This paper derives and compares different definitions of conserved charges in asymptotically AdS spacetimes, establishing agreement with some existing methods and clarifying differences with others, supported by a Hamiltonian and perturbation analysis.

Contribution

The paper provides a Hamiltonian derivation of conserved charges in asymptotically AdS spacetimes and compares it with existing definitions, clarifying their relationships and differences.

Findings

Our definition agrees with Ashtekar et al, spinor, and Henneaux-Teitelboim methods.

Disagreement with the counterterm subtraction method is only a constant offset.

Boundary conditions are justified through linear perturbation analysis.

Abstract

We derive hamiltionian generators of asymptotic symmetries for general relativity with asymptotic AdS boundary conditions using the ``covariant phase space'' method of Wald et al. We then compare our results with other definitions that have been proposed in the literature. We find that our definition agrees with that proposed by Ashtekar et al, with the spinor definition, and with the background dependent definition of Henneaux and Teitelboim. Our definition disagrees with the one obtained from the ``counterterm subtraction method,'' but the difference is found to consist only of a ``constant offset'' that is determined entirely in terms of the boundary metric. We finally discuss and justify our boundary conditions by a linear perturbation analysis, and we comment on generalizations of our boundary conditions, as well as inclusion of matter fields.