Teleparallel Gravitoelectromagnetism: The Role of Boosts in the Schwarzschild Geometry

We study the effects of boosts on the gravitoelectric and gravitomagnetic fields, as described in the Teleparallel Equivalent of General Relativity context, and use the Schwarzschild geometry as a primer example, to reaffirm the definitions of the two fields. To draw a parallel with Electrodynamics, we consider the well-known effect of a boost to an observer moving relative to an electrical point charge at rest. The main conclusion is that in the linear regime, when measured from a reference frame under the effect of a boost towards x, the gravitoelectromagnetic components with algebraic index equal to zero are quite analogous to those of Electromagnetism.