Conserved Quantities in Kerr-anti-de Sitter Spacetimes in Various Dimensions

TL;DR

This paper calculates conserved charges in Kerr-anti-de Sitter spacetimes across various dimensions using two methods, revealing differences in global charges in odd dimensions and discussing implications for the AdS/CFT correspondence.

Contribution

It compares conformal and counterterm methods for conserved charges in Kerr-AdS spacetimes, highlighting differences in global charges in odd dimensions.

Findings

Conserved charges differ by a constant in odd dimensions.

Rotational charges are consistent across methods.

Implications for AdS/CFT are discussed.

Abstract

We compute the conserved charges for Kerr anti-de Sitter spacetimes in various dimensions using the conformal and the counterterm prescriptions. We show that the conserved charge corresponding to the global timelike killing vector computed by the two methods differ by a constant dependent on the rotation parameter and cosmological constant in odd spacetime dimensions, whereas the charge corresponding to the rotational killing vector is the same in either approach. We comment on possible implications of our results to the AdS/CFT correspondence.