Conserved charges in (Lovelock) gravity in first order formalism
Journal
Physical Review D
Date Issued
April 6, 2010
Author(s)
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.
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.