Quasilocal conserved charges in the presence of a gravitational Chern-Simons term

Abstract

We extend our recent work on the quasilocal formulation of conserved charges to a theory of gravity containing a gravitational Chern-Simons term. As an application of our formulation, we compute the off-shell potential and quasilocal conserved charges of some black holes in threedimensional topologically massive gravity. Our formulation for conserved charges reproduces very effectively the well-known expressions on conserved charges and the entropy expression of black holes in the topologically massive gravity. *

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

“…This ADM formalism has been extended to the covariant and higher curvature gravity theories by Abbott, Deser and Tekin [36][37][38]. There was a non-trivial generalization of the ADT charge formalism by promoting to the off-shell level and including non-covariant term like a gravitational Chern-Simons term [44,45]. In [74] the quasi-local conserved charge for the Chern-Simons-like theories of gravity (110) has been constructed with the first order formalism.…”

“…These energies can be represented by terms of left and right central charges and their temperatures respectively. 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].…”

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

“…This formalism is established on a metric formalism of gravity theories and has been extended to noncovariant theories in [9]. But it is well known that we can write down the gravity theories in the first order formalism.…”

“…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.…”

“…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.…”