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

TL;DR

This work analyzes conserved quantities for Kerr–anti-de Sitter spacetimes across dimensions using both the conformal and counterterm formalisms. It derives expressions for conserved charges from the electric part of the Weyl tensor and from the holographic boundary stress tensor, applying the Kraus–Larsen–Siebelink counterterm expansion up to $d=9$. A key finding is that, in odd dimensions, the mass computed by the two methods differs by a Casimir-energy term dependent on the rotation parameter $a$ and the AdS scale $\ell$, while the angular momentum is the same in both approaches; these results are consistent with the Gibbs–Duhem relation. The paper discusses AdS/CFT implications and notes the absence of a Casimir term for the rotational KVF, suggesting further investigations into more general AAdS spacetimes and multiple rotation parameters.

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.