Quasilocal conserved charges and holography

Abstract

We construct a quasi-local formalism for conserved charges in a theory of gravity in the presence of matter fields which may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion and so it is irrespective of ambiguities in the total derivatives of the Lagrangian. By using identically conserved currents, we show that this formalism leads to the same expressions of conserved charges as those in the covariant phase space approach. At the boundary of the asymptotic AdS space, we also introduce an identically conserved boundary current which has the same structure as the bulk current and then show that this boundary current gives us the holographic conserved charges identical with those from the boundary stress tensor method. In our quasi-local formalism we present a general proof that conserved charges from the bulk potential are identical with those from the boundary current. Our results can be regarded as the extension of the existing results on the equivalence of conserved charges by the covariant phase space approach and by the boundary stress tensor method. *

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

“…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.…”

Revisiting the ADT mass of the five-dimensional rotating black holes with squashed horizons

“…That is to say, the background metric is off-shell. However, strictly speaking, the original ADT current requires that the background metric is on-shell although the potential corresponding to such a current is in agreement with the off-shell generalised one in [37][38][39][40]. Thus, in order to fully obey the spirit of the usual ADT formalism [32][33][34][35][36], here we shall look for an appropriate on-shell reference metric to recalculate the ADT mass of these black holes.…”

“…For the Lagrangian (4.1), the potentials associated with the U(1) gauge field and the scalar field, derived in terms of the off-shell ADT method in Refs. [38,40,42,43], are suitable for the desired ones of the fields A μ and ϕ in the conventional ADT formalism. As a result, we directly present the total ADT potential Q μν EMD relevant to the Lagrangian (4.1) on the fixed reference background (ḡ μν ,Ā μ ,φ) in the following form: …”

Scaling symmetry and scalar hairy rotatingAdS3black holes

“…[22,18] to obtain the conserved charge J H for ξ R on the horizon. The upshot of the asymptotic Killing vector case is the existence of the additional term A in the quasi-local ADT potential as…”