Covariance properties and regularization of conserved currents in tetrad gravity

TL;DR

This paper examines the covariance and regularization of gravitational energy-momentum in tetrad gravity, proposing a method to obtain finite total energy values for solutions with asymptotically flat spacetime.

Contribution

It introduces a regularization technique for the gravitational energy-momentum in tetrad gravity, ensuring finite total energy calculations for asymptotically flat solutions.

Findings

Proposed a natural regularization method for energy-momentum

Demonstrated regularization on explicit Einstein solutions

Ensured covariance under Lorentz transformations

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 energy-momentum 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.