A Dirichlet-type integral on spheres, applied to the fluid/gravity correspondence

Abstract

We evaluate an analogue of an integral of Dirichlet over the sphere S^D, but with an integrand that is independent of [(D + 1)/2] Killing coordinates. As an application, we evaluate an integral that arises when comparing a conformal fluid on S^D and black holes in (D + 2)-dimensional anti-de Sitter spacetime.

5 pages