Local Lorentz transformations and Thomas effect in general relativity

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.