Conserved charges of higher D Kerr-AdS spacetimes

Rotating solutions of cosmological Einstein gravity in D dimensions, R-mu v = (D - 1)Lambda g(mu v), have been constructed recently [1, 2], extending earlier A = 0 solutions of [3], themselves generalizations of the well-known D = 4 metrics of [4] and [5], and of [6] in D = 5. These geometries provide a useful application of our recent generalized 'conserved charge' definitions, which are also extensions-of the original ADM [7], and AD [9] charges-to cover wider classes of actions [9, 11]: we will compute the energy and angular momenta of these new solutions. Gravity theories have been historically endowed with a variety of seemingly different charge definitions, with different degrees of applicability and coordinate invariance. This topic has also seen much very recent activity, for example [12]. A summary and comparison of some of them is given in [13] which also includes a computation of the charges for Kerr-AdS black holes, using thermodynamic arguments; see also [14, 16]. Our results will agree with those, but we emphasize that in a general context, certain coincidences between charge definitions are suspect: for example, the frequently invoked 'Komar' charges, are in general not applicable, being highly gauge dependent [17].