Covariant Symplectic Structure and Conserved Charges of New Massive Gravity

Abstract

We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a Poincare invariant 2-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory. Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for spacetimes with non-constant curvature backgrounds, by using the diffeomorphism invariance of the symplectic 2-form. As an example, we calculate the conserved charges of some solutions of New Massive Gravity (NMG) and compare the results with the previous works.

18 pages, No figures, RevTEX4.1; ver 2: minor corrections, version accepted for publication in Physical Review D

References in corpus (9)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Lifshitz Black Hole in Three Dimensions
• Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
• Warped AdS_3 black holes in new massive gravity
• A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds
• On the thermodynamics of Lifshitz black holes
• Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds
• Covariant Symplectic Structure and Conserved Charges of Topologically Massive Gravity

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• Conserved Charges in Extended Theories of Gravity
• Revisiting Conserved Charges in Higher Curvature Gravitational Theories
• Coupling Constants as Conserved Charges in Black Hole Thermodynamics
• First law of black hole thermodynamics and Smarr formula with a cosmological constant