  The tetrad method is used for an introduction of local Lorentz frames and a
detailed analysis of local Lorentz transformations. A formulation of equations
of motion in local Lorentz frames is based on the Pomeransky-Khriplovich
gravitoelectromagnetic fields. These fields are calculated in the most
important special cases and their local Lorentz transformations are determined.
The local Lorentz transformations and the Pomeransky-Khriplovich
gravitoelectromagnetic fields are applied for a rigorous derivation of a
general equation for the Thomas effect in Riemannian spacetimes and for a
consideration of Einstein's equivalence principle and the Mathisson force.
