Conserved Charges in Asymptotically Locally AdS Spacetimes via the Katz Method
Abstract: The Katz boundary term provides a well-defined variational principle under Dirichlet boundary conditions and, when combined with a subtraction of the action evaluated on a background, yields finite Noether charges and a finite on-shell action. This boundary term is constructed from the dynamical metric and the difference between the Christoffel symbols associated with the dynamical manifold and a reference background. So far, this method has been tested only for specific classes of solutions. In this work, using the Fefferman–Graham gauge, we show that the finiteness of conserved charges can be proven for families of asymptotically locally Anti–de Sitter spacetimes in general relativity. The finiteness of the charges can be established in arbitrary dimensions; however, the prescription for defining the background in this framework distinguishes between even and odd spacetime dimensions.