  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.

High Energy Physics - Theory