Quasi-local conserved charges in the Einstein-Maxwell theory

In this paper we consider the Einstein-Maxwell theory and define a combined transformation composed of diffeomorphism and U(1) gauge transformation. For generality, we assume that the generator χ of such transformation is field-dependent. We define the extended off-shell ADT current and then off-shell ADT charge such that they are conserved off-shell for the asymptotically field-dependent symmetry generator χ. Then, we define the conserved charge corresponding to the asymptotically field-dependent symmetry generator χ. We apply the presented method to find the conserved charges of the asymptotically AdS3 space-times in the context of the Einstein-Maxwell theory in three dimensions. Although the usual proposal for the quasi local charges provides divergent global charges for the Einstein-Maxwell theory with negative cosmological constant in three dimensions, here we avoid this problem by introducing proposed combined transformation χ.