Mass and angular momentum of black holes in a new massive gravity

Abstract

We obtain mass and angular momentum of black holes as conserved charges in three dimensional new massive gravity, after presenting the explicit expression for the potential of the conserved charges. This confirms the expression of those charges obtained in several ways, in particular through AdS/CFT correspondence, and shows us that the first law of black hole thermodynamics is valid in these black holes. We also comment about conserved charges in new type black holes with the emphasis on the AdS/CFT correspondence as guiding principle.

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

“…An interesting method to find quasi-local conserved charges can be represented using the relation between off-shell ADT potential and linearized Noether potential [44,45]. There are many works to obtain mass and angular momentum of black holes on Ad S background using methods mentioned above [43][44][45][46][47][48][49][50][51][52][53]. Also there have been some studies about conserved charges, central charges and the behavior of the correlation functions of dual CFT by using the holographic renormalization method [54,55].…”

Quasi-local conserved charges in Lorenz–diffeomorphism covariant theory of gravity

“…As is well known, the concept of conserved charges of gravity theories is related to the concept of the Noether charges corresponding to the Killing vectors which are admitted by solutions of a theory. There are several approaches to obtain the mass and angular momentum of black holes solutions of different gravity theories [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. According to the Arnowitt, Deser, and Misner formalism (ADM formalism) [3] one can obtain the conserved charges of an asymptotically flat spacetime solution of a general theory of relativity, but this is not a covariant method.…”

“…This method is a covariant formalism; it is known as the Abbott-Deser-Tekin (ADT) formalism [1,2,[4][5][6]. Thus the ADT formalism is applicable in the general higher curvature and higher derivative theories of gravity [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Another method is the Brown-York formalism [7], which is based on a quasi-local concept, but this approach also is not covaria e-mail: hamed.adami@yahoo.com b e-mail: rezakord@ipm.ir ant.…”

Holographic renormalization and stress tensor in new massive gravity

“…Even with these studies there are some missing parts in the analysis and it is also desirable to study holographic renormalization in the unified manner. One may note that there is another special point other than critical point in NMG, which is related to the existence of the so-called new type black holes [6,12,40,41,42]. At this special point, it has been known that a different fall-off of bulk modes is allowed.…”