Gravitomagnetism in teleparallel gravity
  The assumption that matter charges and currents could generate fields, which are called, by analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dates from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism behind it seems to be more appropriated to deal with phenomena related to observers.   As our main results, we have obtained, for the first time, the exact expressions for the gravito-electromagnetic fields for the Schwarzschild solution that in the linear approximation become the usual expected ones. To improve our understanding about these fields, we have also studied the geometry produced by a spherical rotating shell in slow motion and weak field regime. Again, the expressions obtained are in complete agreement with those of electromagnetism. 
E. P. Spaniol and V. C. de Andrade