Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor

TL;DR

This paper proposes a new gravitational energy expression combining tetrad and Einstein pseudotensor methods, resulting in a positive energy property and improved energy calculations in gravitating systems.

Contribution

It introduces a novel energy-momentum expression that merges tetrad and Einstein pseudotensor approaches, enhancing gravitational energy evaluation.

Findings

The combined expression yields positive gravitational energy.

It improves upon previous energy-momentum definitions.

The approach bridges orthonormal and holonomic frames.

Abstract

The energy-momentum for a gravitating system can be considered by the tetard teleparalle gauge current in orthonormal frames. Whereas the Einstein pseudotensor used holonomic frames. Tetrad expression itself gives a better result for gravitational energy than Einstein's. Inspired by an idea of Deser, we found a gravitational energy expression which enjoys the positive energy property by combining the tetrad expression and the Einstein pseudotensor, i.e., the connection coefficient has a form appropriate to a suitable intermediate between orthonormal and holonomic frames.