Local Lorentz transformations and Thomas effect in general relativity

TL;DR

This paper uses the tetrad method to analyze local Lorentz transformations and derive the Thomas effect in general relativity, connecting gravitoelectromagnetic fields with particle motion and fundamental principles.

Contribution

It provides a detailed formulation of local Lorentz transformations and equations of motion using gravitoelectromagnetic fields within the tetrad framework, applying these to the Thomas effect in curved spacetime.

Findings

Derived a general equation for the Thomas effect in Riemannian spacetimes.

Calculated gravitoelectromagnetic fields in key special cases.

Connected local Lorentz transformations with Einstein's equivalence principle and the Mathisson force.

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.