Quasi-local 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.

27 pages, LaTeX; v2 references added; v3 version to appear in PRD

References in corpus (8)

• Surface charge algebra in gauge theories and thermodynamic integrability
• Black hole mass and angular momentum in topologically massive gravity
• Black Hole Entropy in the presence of Chern-Simons Terms
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions
• The CFT-interpolating Black Hole in Three Dimensions
• Quasi-local charges and asymptotic symmetry generators
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Cited by in corpus (7)

• Black hole conserved charges in Generalized Minimal Massive Gravity
• Thermodynamics of static dyonic AdS black holes in the $\omega$-deformed Kaluza-Klein gauged supergravity theory
• Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities
• General formulas for conserved charges and black hole entropy in Chern-Simons-like theories of gravity
• Frame-independent holographic conserved charges
• Revisit to Thermodynamic Relations in the AdS/CMT Models
• Off-Shell ADT Conserved Quantities in Palatini Gravity