Conserved charges in (Lovelock) gravity in first order formalism

Abstract

We derive conserved charges as quasilocal Hamiltonians by covariant phase space methods for a class of geometric Lagrangians that can be written in terms of the spin connection, the vielbein, and possibly other tensorial form fields, allowing also for nonzero torsion. We then recalculate certain known results and derive some new ones in three to six dimensions hopefully enlightening certain aspects of all of them. The quasilocal energy is defined in terms of the metric and not its first derivatives, requiring ``regularization'' for convergence in most cases. Counterterms consistent with Dirichlet boundary conditions in first order formalism are shown to be an efficient way to remove divergencies and derive the values of conserved charges, the clear-cut application being metrics with anti--de Sitter (or de Sitter) asymptotics. The emerging scheme is: all is required to remove the divergencies of a Lovelock gravity is a boundary Lovelock gravity.