Gravitoelectromagnetism in Teleparallel Equivalent of General Relativity: A New Alternative

TL;DR

This paper proposes a new definition of gravitoelectromagnetic fields in TEGR using torsions, leading to a complete set of Maxwell-like equations and explicit field expressions in Schwarzschild spacetime and gravitational waves.

Contribution

It introduces an alternative approach to define gravitoelectromagnetic fields in TEGR using torsions, resulting in a complete set of Maxwell-like equations.

Findings

Derived explicit gravitoelectromagnetic fields in Schwarzschild spacetime

Obtained Maxwell-like equations for gravitoelectromagnetism in TEGR

Provided expressions for gravitational waves in the new framework

Abstract

Spaniol and Andrade introduced grvitoelectromagnetism in TEGR by considering superpotentials, times the determinant of tetrads, as the gravitoelectromagnetic fields. However, since this defined gravitoelectromagnetic field strength does not give rise to a complete set of Maxwell-like equations, we propose an alternative definition of the gravitoelectromagnetic field strength: instead of superpotentials, torsions are taken as the gravitoelectromagnetic field strengths. Based on this new proposal we are able to derive a complete set of Maxwell-like equations. We then apply them to obtain explicit expressions of the gravitoelectromagnetic fields both in Schwarzchilds spacetime and for gravitational waves.