Conserved charges in (Lovelock) gravity in first order formalism
arXiv:1004.3582 · doi:10.1103/PhysRevD.81.084013
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.
20 pages, no figures
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