Conserved charges in (Lovelock) gravity in first order formalism

TL;DR

This paper develops a covariant phase space method to derive conserved charges in Lovelock gravity using first order formalism, addressing divergences with boundary counter-terms, especially for asymptotically AdS or dS spacetimes.

Contribution

It introduces a new approach to compute quasi-local conserved charges in Lovelock gravity within the first order formalism, including non-zero torsion and boundary counter-terms.

Findings

Derived conserved charges as quasi-local Hamiltonians.

Re-calculated known results and derived new ones in 3-6 dimensions.

Showed boundary Lovelock gravity removes divergences effectively.

Abstract

We derive conserved charges as quasi-local 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 non-zero torsion. We then re-calculate certain known results and derive some new ones in three to six dimensions hopefully enlightening certain aspects of all of them. The quasi-local energy is defined in terms of the metric and not its first derivatives, requiring `regularization' for convergence in most cases. Counter-terms 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 AdS (or dS) asymptotics. The emerging scheme is: all is required to remove the divergencies of a Lovelock gravity is a boundary Lovelock gravity.