Lorentz Covariant Theory of Precise Doppler Measurements

TL;DR

This paper develops a Lorentz covariant framework for precise Doppler measurements using retarded solutions of Einstein's equations, providing exact light propagation solutions and formulas for gravitational frequency shifts applicable to various astrophysical and space navigation scenarios.

Contribution

It introduces an exact solution for light propagation in arbitrary moving gravitational fields and formulates a Lorentz covariant theory of Doppler measurements extending current models.

Findings

Derived explicit formula for gravitational frequency shift.

Extended applicability to gravitational lensing and spacecraft Doppler tracking.

Developed post-Newtonian theory for relativistic effects in binary and planetary systems.

Abstract

The Lorentz covariant theory of precise Doppler measurements (PDM) based on the retarded Li\'{e}nard-Wiechert solution of the Einstein equations is described. An exact solution of equations of light propagation in the field of arbitrary moving bodies, which drastically extends the range of applicability of the new theory of PDM, is obtained. An explicit formula for the gravitational shift of frequency is given in analytic form. The limiting cases of the Doppler observations in gravitational lensing and of the spacecraft's Doppler tracking are described in more detail. We also present the post-Newtonian theory of the PDM developed for searching relativistic effects in close optical binaries and massive planetary systems.