Black hole mass and Hamilton-Jacobi counterterms

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 expression Ω = E−TS−ΦIQI continues to hold in general in the presence of arbitrary matter couplings to gravity.