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

TL;DR

This paper evaluates a Dirichlet-type integral on spheres with applications to the fluid/gravity correspondence, specifically comparing conformal fluids on spheres and black holes in anti-de Sitter spacetime.

Contribution

It introduces a new integral evaluation method on spheres and applies it to relate conformal fluids and black hole solutions in higher-dimensional AdS spacetime.

Findings

Derived a new integral formula on spheres independent of certain Killing coordinates.

Applied the integral to compare conformal fluids and black holes in AdS spacetime.

Provided insights into the fluid/gravity correspondence in higher dimensions.

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.