Gravitoelectromagnetism in teleparallel equivalent of general relativity: A new alternative

Spaniol and Andrade introduced gravitoelectromagnetism 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 Schwarzschilds spacetime and for gravitational waves.