Covariance properties and regularization of conserved currents in tetrad gravity

Abstract

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energymomentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.

The teleparallel equivalent of general relativity

“…In order to prove the identity, it is easier to start with the left-hand side of Eq. (28) and arrive at the latter expression. For this purpose, the following three identities are helpful.…”

“…are useful in obtaining 1 2 e R aμ (e) − 1 2 e aμ R(e) by means of algebraic manipulations of the left-hand side of (28). We note that by means of these identities, one may always transform the standard form of Einstein's equations for a general (non-asymptotically flat) space-time into the field equations of the TEGR.…”

“…[25,26]. Teleparallel gravity has been readdressed by Obukhov and Pereira [27] in the geometrical framework of metric-affine theories, and further reconsidered by Obukhov and Rubilar [28,29], with the purpose of investigating the transformation (covariance) properties and conserved currents in tetrad theories of gravity. They analysed the problem of consistently defining the gravitational energy-momentum and, in particular, the problem of regularization of the expression of the gravitational energy-momentum (see also Ref.…”

“…Consequently, a metric tensor g μν that is a solution of Einstein's equations is also a solution of Eq. (28). For a given space-time metric, there exists an infinity of allowed frames.…”

Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

“…The previous results, as well as an overview of the earlier literature can be found in [1,2], see also the extensive reference list in [3]. More specifically, we will be interested in the conserved currents and charges associated with vector fields that generate arbitrary diffeomorphisms on the spacetime manifold.…”