The role of observers in the measurement of teleparallel gravitoelectromagnetic fields in Schwarzschild spacetime

In the context of the teleparallel equivalent of general relativity (TEGR) we investigate the role of local observers, associated with tetrad fields, in the 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 Schwarzschild space-time. Then, we investigate whether it is possible to distinguish between this situation and that of an observer at rest in Minkowski space-time. We conclude that, although there are non-zero components of the fields obtained in the case of a free fall, its dynamical effect, measured by the gravitational Lorentz force, is zero. Moreover, the gravitational field energy obtained from the GEM fields for an observer freely falling in Schwarzschild spacetime, is zero. These results are in complete agreement with the equivalence principle.