The Brown-York mass of black holes in Warped Anti-de Sitter space

Abstract

We give a direct computation of the mass of black holes in Warped Anti-de Sitter space (WAdS) in terms of the Brown-York stress-tensor at the boundary. This permits to explore to what extent the holographic renormalization techniques can be applied to such type of deformation of AdS. We show that, despite some components of the boundary stress-tensor diverge and resist to be regularized by the introduction of local counterterms, the precise combination that gives the quasilocal energy density yields a finite integral. The result turns out to be in agreement with previous computations of the black hole mass obtained with different approaches. This is seen to happen both in the case of Topologically Massive Gravity and of the so-called New Massive Gravity. Here, we focus our attention on the latter. We observe that, despite other conserved charges diverge in the near boundary limit, the finite part in the large radius expansion captures the physically relevant contribution. We compute the black hole angular momentum in this way and we obtain a result that is in perfect agreement with previous calculations.