Kerr de Sitter Spacetimes in Various Dimension and dS/CFT Correspondence

TL;DR

This paper analyzes Kerr-de Sitter black holes across various dimensions, calculating finite conserved charges and exploring their properties within the dS/CFT correspondence framework.

Contribution

It introduces a counterterm method to obtain finite actions and computes conserved charges for Kerr-dS spacetimes with multiple rotational parameters in different dimensions.

Findings

Total action is finite after adding counterterms.

Total angular momentum is independent of boundary radius.

Mass and angular momentum are computed explicitly in multiple dimensions.

Abstract

We consider the Kerr-de Sitter (Kerr-dS) black hole in various dimensions. Introducing a counterterm, we show that the total action of these spacetimes are finite. We compute the masses and the angular momenta of Kerr-dS spaces with one rotational parameter in four, five and seven dimensions. These conserved charges are also computed for the case of Kerr-dS space with two rotational parameters in five dimensions. Although the angular momentum density due to the counterterm is nonzero, it gives a vanishing contribution to the total angular momentum. We also find that the total angular momentum of the spacetime is independent of the radius of the boundary for all cases, a fact that is not true for the total mass of the system.