Boundary stress tensor and counterterms for weakened AdS_3 asymptotic in New Massive Gravity

Abstract

Resorting to the notion of a stress tensor induced on the boundary of a spacetime, we compute the conserved charges associated to exact solutions of New Massive Gravity that obey weakened versions of AdS_3 asymptotic boundary conditions. The computation requires the introduction of additional counterterms, which play the role of regularizing the semiclassical stress tensor in the boundary theory. We show that, if treated appropriately, different ways of prescribing asymptotically AdS_3 boundary conditions yield finite conserved charges for the solutions. The consistency of the construction manifests itself in that the charges of hairy asymptotically AdS_3 black holes computed by this holography-inspired method exactly match the values required for the Cardy formula to reproduce the black hole entropy. We also consider new solutions to the equations of motion of New Massive Gravity, which happen to fulfill Brown-Henneaux boundary conditions despite not being Einstein manifolds. These solutions are shown to yield vanishing boundary stress tensor. The results obtained in this paper can be regarded as consistency checks for the prescription proposed in arXiv:1001.3598.