Quasilocal energy for three-dimensional massive gravity solutions with chiral deformations of AdS boundary conditions

TL;DR

This paper explores solutions in three-dimensional critical gravity with weakened asymptotic conditions, defining a quasilocal stress-tensor to compute finite conserved charges despite strong boundary deformations.

Contribution

It introduces exact solutions with weaker fall-off conditions in 3D critical gravity and calculates their conserved charges using a quasilocal stress-tensor.

Findings

Solutions have finite mass and angular momentum despite weak asymptotic fall-off

Defined a quasilocal stress-tensor for these solutions

Demonstrated non-vanishing charges in deformed AdS3 backgrounds

Abstract

We consider critical gravity in three dimensions; that is, the New Massive Gravity theory formulated about Anti-de Sitter (AdS) space with the specific value of the graviton mass for which it results dual to a two-dimensional conformal field theory with vanishing central charge. As it happens with Kerr black holes in four-dimensional critical gravity, in three-dimensional critical gravity the Banados-Teitelboim-Zanelli black holes have vanishing mass and vanishing angular momentum. However, provided suitable asymptotic conditions are chosen, the theory may also admit solutions carrying non-vanishing charges. Here, we give simple examples of exact solutions that exhibit falling-off conditions that are even weaker than those of the so-called Log-gravity. For such solutions, we define the quasilocal stress-tensor and use it to compute conserved charges. Despite the drastic deformation of AdS3 asymptotic, these solutions have finite mass and angular momentum.