Conserved charges in (Lovelock) gravity in first order formalism
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.
Cite
@article{arxiv.1004.3582,
title = {Conserved charges in (Lovelock) gravity in first order formalism},
author = {Elias Gravanis},
journal= {arXiv preprint arXiv:1004.3582},
year = {2010}
}
Comments
20 pages, no figures