Coframe energy-momentum current. Algebraic properties

TL;DR

This paper investigates the algebraic properties of the conserved energy-momentum current in coframe (teleparallel) gravity, revealing its relation to the energy-momentum tensor and its unique features compared to electromagnetic fields.

Contribution

It analyzes the algebraic structure of the covariant conserved current in teleparallel gravity and clarifies its relation to the energy-momentum tensor for various parameters.

Findings

The tensor associated with the coframe current is traceless.

It generally has a non-vanishing antisymmetric part.

The current encompasses both energy-momentum and spin properties.

Abstract

The coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy-momentum current witch is covariant under all symmetries of the three-parameter Lagrangian. In this paper we study the relation between the covector valued current and the energy-momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy-momentum as well as the rotational (spin) properties of the field.