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The role of observers in the measurement of the Teleparallel Gravitoelectromagnetic fields in different geometries

In the context of the Teleparallel Equivalent of General Relativity (TEGR) we have investigated the role of local observers, associated with tetrad fields, in description of the gravitational interaction through the concepts of the gravitoelectric (GE) and gravitomagnetic (GM) fields. We start by analyzing the gravitoelectromagnetic (GEM) fields obtained from an observer freely falling in the Schwarzschild space-time. Then, we investigated whether it is possible to distinguish between this situation and to be at rest in the Minkowski space-time. We conclude that, although there are non-zero components for the fields obtained for the case of free fall, its dynamical effect, measured by the gravitational Lorentz force, is null. Moreover, the gravitational field energy obtained from the GEM fields for an observer freely falling in the Schwarzschild spacetime is zero. These results are in complete agreement with the equivalence principle.