Asymptotically anti de Sitter spacetimes in three dimensions

TL;DR

This paper analyzes three-dimensional asymptotically Anti de Sitter spacetimes, formulating covariant boundary conditions, constructing conserved charges, and exploring the trace anomaly related to the Brown-York stress tensor.

Contribution

It introduces a covariant formulation of boundary conditions and constructs global charges, revealing the trace anomaly matches the Brown-Henneaux central charge.

Findings

Charges are conserved for asymptotic Killing vectors.

The boundary stress-energy tensor is not traceless.

The trace anomaly equals the Brown-Henneaux central charge.

Abstract

We revisit the asymptotically Anti de Sitter spacetimes in three dimensions. Using the conformal-completion technique, we formulate the boundary conditions in a covariant fashion and construct the global charges associated with the asymptotic symmetries. The charges so constructed are conserved for the asymptotic Killing vectors fields but are not conserved for the asymptotic conformal Killing vector fields. The quantity integrated to obtain the global charge is interpreted as the Brown-York boundary stress-energy tensor and it is found not to be traceless. The trace is interpreted as the trace anomaly and it turns out to be the same as the Brown-Henneaux central charge.