Explicit exact expression for the Thomas precession

TL;DR

This paper derives an explicit exact expression for the Thomas precession in special relativity, providing a compact formula for the rotation angle resulting from two Lorentz boosts, with applications to Gaia data analysis.

Contribution

It presents a new explicit formula for the Thomas precession angle and rotation matrix, enhancing understanding of relativistic effects in astrophysical contexts.

Findings

Explicit orthogonal matrix for Thomas precession derived

Compact formula for the rotation angle obtained

Application to Gaia data for testing Lorentz invariance

Abstract

This work gives an explicit exact expression for the Thomas precession arising in the framework of Special Theory of Relativity as the spatial rotation resulting from two subsequence Lorentz boosts. The final result for the orthogonal matrix of Thomas precession is given by Eqs. (21)--(25). A trivial calculation leads to the compact formula (26) for the angle of rotation due to Thomas precession. In the framework of Gaia the special-relativistic Thomas precession is an important step in the derivation of an aberrational formula with the Mansouri-Sexl parameters. The latter formula will be used to test the Local Lorentz Invariance with Gaia data as will be explained elsewhere.