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Paper IPM / P / 14175  


Abstract:  
We provide a general formulation for calculating conserved charges for solutions to generally covariant gravitational theories with possibly other internal gauge symmetries, in any dimensions and with generic asymptotic behaviors. These solutions are generically specified by a number of exact (continuous, global) symmetries and some parameters. We define parametric variations as field perturbations generated by variations of the solution parameters. Employing the covariant phase space method, we establish that the set of these solutions (up to pure gauge transformations) form a phase space, the solution phase space, and that the tangent space of this phase space includes the parametric variations. We then compute conserved charge variations associated with the exact symmetries of the family of solutions, caused by parametric variations. Integrating the charge variations over a path in the solution phase space, we define the conserved charges. In particular, we revisit black hole entropy as a conserved charge and the derivation of the first law of black hole thermodynamics. We show that the solution phase space setting enables us to define black hole entropy by an integration over any compact, codminesion2, smooth spacelike surface encircling the hole, as well as to a natural generalization of Wald and IyerWald analysis to cases involving gauge fields.
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