The gravitational energy-momentum tensor and the gravitational pressure

TL;DR

This paper derives a unique, conserved, and traceless energy-momentum tensor for gravity within teleparallel gravity, and demonstrates its use in defining gravitational pressure.

Contribution

It establishes a consistent, unique gravitational energy-momentum tensor in teleparallel gravity and connects it to gravitational pressure.

Findings

The tensor is conserved and traceless.

It provides expressions for gravitational energy and momentum.

Spatial components define gravitational pressure.

Abstract

In the framework of the teleparallel equivalent of general relativity it is possible to establish the energy-momentum tensor of the gravitational field. This tensor has the following essential features: (1) it is identified directly in Einstein's field equations; (2) it is conserved and traceless; (3) it yields expressions for the energy and momentum of the gravitational field; (4)it is free of second (and highest) derivatives of the field variables; (5) the gravitational and matter energy-momentum tensors take place in the field equations on the same footing; (6) it is unique. However, it is not symmetric. We show that the spatial components of this tensor yield a consistent definition of the gravitational pressure.