Kerr–de Sitter spacetimes in various dimensions and dS/CFT correspondence

We consider the Kerr–de Sitter (Kerr-dS) black hole in various dimensions. Introducing a counterterm, we show that the total actions 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.