Abstract
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.
Highlights
Methods of description of gravitational phenomena based on an introduction of tetrads are often used in contemporary gravity
Since the metric of local Lorentz frame (LLF) is locally Minkowskian, a transition from one LLF to another one is defined by an appropriate Lorentz transformation
The results presented explicitly show the possibility of the local Lorentz transformations of the gravitoelectromagnetic fields and the equivalence of all tetrads
Summary
Methods of description of gravitational phenomena based on an introduction of tetrads are often used in contemporary gravity. Telegdi equation for a Dirac particle and to the equation of motion of a charged particle This similarity has made it possible to derive general formulas for the gravitoelectromagnetic fields [13] defined in an anholonomic tetrad frame and describing a relativistic particle in an arbitrarily strong gravitational field or in a noninertial frame. The MP and Pomeransky-Khriplovich (PK) equations agree when one can neglect the mutual influence of particle and spin motion leading to the aforementioned violation [4] This circumstance substantiates the results obtained by Pomeransky and Khriplovich and brings a possibility of a wide application of the approach based on the PK gravitoelectromagnetic fields. We fulfill the general description of the Thomas precession in gravity with the use of the local Lorentz transformations and the gravitoelectromagnetic fields. Commas and semicolons before indices denote partial and covariant derivatives, respectively
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