Black hole mass and Hamilton-Jacobi counterterms

TL;DR

This paper uses holographic renormalization and Hamilton-Jacobi methods to compute finite masses of R-charged black holes in various dimensions, confirming thermodynamic laws hold with matter couplings.

Contribution

It demonstrates a systematic way to obtain finite black hole masses in gauged supergravities using boundary counterterms derived from Hamilton-Jacobi analysis.

Findings

Counterterms render black hole masses finite in multiple dimensions.

Black hole thermodynamics and the first law hold with matter couplings.

Method applies to R-charged black holes in gauged supergravities.

Abstract

We apply the method of holographic renormalization to computing black hole masses in asymptotically anti-de Sitter spaces. In particular, we demonstrate that the Hamilton-Jacobi approach to obtaining the boundary action yields a set of counterterms sufficient to render the masses finite for four, five, six and seven-dimensional R-charged black holes in gauged supergravities. In addition, we prove that the familiar black hole thermodynamical expressions and in particular the first law continues to holds in general in the presence of arbitrary matter couplings to gravity.