Conserved Charges in Even Dimensional Asymptotically locally Anti-de Sitter Space-times

TL;DR

This paper derives a new formula for calculating conserved charges in even-dimensional asymptotically locally Anti-de Sitter space-times, generalizing previous methods and applying it to various solutions including Taub-Bolt-AdS and Kerr-AdS.

Contribution

It introduces a generalized formula for conserved charges in even-dimensional ALAdS space-times based on Wald and Zoupas' definition, extending prior approaches.

Findings

The new formula agrees with background subtraction and boundary counterterm methods.

Computed masses of Taub-Bolt-AdS and Kerr-AdS solutions in various dimensions.

Provided mass calculations for unwrapped brane solutions in any dimension.

Abstract

Based on the recent paper hep-th/0503045, we derive a formula of calculating conserved charges in even dimensional asymptotically {\it locally} anti-de Sitter space-times by using the definition of Wald and Zoupas. This formula generalizes the one proposed by Ashtekar {\it et al}. Using the new formula we compute the masses of Taub-Bolt-AdS space-times by treating Taub-Nut-AdS space-times as the reference solution. Our result agrees with those resulting from "background subtraction" method or "boundary counterterm" method. We also calculate the conserved charges of Kerr-Taub-Nut-AdS solutions in four dimensions and higher dimensional Kerr-AdS solutions with Nut charges. The mass of (un)wrapped brane solutions in any dimension is given.