Black hole mass and angular momentum in topologically massive gravity

Abstract

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics. *

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

“…Here, we will show that, despite some components of the Brown-York stress-tensor diverge in the near boundary limit and resist to be regularized by the introduction of local counterterms, the integral of the precise combination that gives the definition of the quasilocal energy as a conserved charge yields a finite integral. The result we obtain happens to be in agreement with computations of the black hole mass obtained by different methods [25,30,31]. Finiteness of the conserved charge computed in this way follows from cancellations that occur near the boundary.…”

“…Certainly, WAdS 3 spaces were first obtained as exact solutions to the equations of motion of TMG [25,26]. WAdS 3 space and WAdS 3 black holes are solutions to TMG if the coupling of the Chern-Simons term,…”

“…For instance, WAdS spaces provide gravity duals for condensed matter systems with Schrödinger symmetry [12,13], they are closely related to the geometry of rotating black holes [14,15], and they also appear in relation to many other interesting subjects [16][17][18]. Asymptotically WAdS 3 spaces turn out to be exact solutions of String Theory [19][20][21][22][23] as well as of other models of threedimensional gravity, including Higher-Spin Gravity [24], Topologically Massive Gravity (TMG) [25,26], and New Massive Gravity (NMG) [27]. Here, we will be concerned with the latter: We will consider asymptotically WAdS 3 black holes in NMG.…”

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

“…These results are also the same with [7,8]. The charge variation (43) can be re-expressed by a total variation form.…”

“…The linearization of this theory describes the existence of a single massive graviton mode. This theory also allows some black hole solutions having Ad S asymptotics [7,8]. There have been many investigations for this TMG theory from the viewpoint of Ad S/C FT correspondence [9][10][11][12].…”