Lorentz Covariant Theory of Light Propagation in Gravitational Fields of Arbitrary-Moving Bodies

TL;DR

This paper develops a Lorentz covariant framework for light propagation in weak gravitational fields of moving bodies, providing generalized formulas for time delay, deflection, and redshift applicable to dynamic astrophysical systems.

Contribution

It introduces a new approach using Lienard-Wiechert potentials to model light propagation in arbitrary-moving gravitational fields, extending previous static or uniform motion models.

Findings

Derived general expressions for gravitational time delay, deflection angle, and redshift.

Included velocity-dependent terms in gravitational lens equations.

Applied the theory to binary pulsars and solar system astrometry.

Abstract

The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert presentation of the metric tensor. A new approach for integrating the equations of motion of light particles depending on the retarded time argument is applied. In an approximation which is linear with respect to the universal gravitational constant, G, the equations of light propagation are integrated by quadratures and, moreover, an expression for the tangent vector to the perturbed trajectory of light ray is found in terms of instanteneous functions of the retarded time. General expressions for the relativistic time delay, the angle of light deflection, and gravitational red shift are derived. They generalize previously known results for the case of static or uniformly moving bodies. The most important applications of the theory are given. They include a discussion of the velocity dependent terms in the gravitational lens equation, the Shapiro time delay in binary pulsars, and a precise theoretical formulation of the general relativistic algorithm of data processing of radio and optical astrometric measurements in the non-stationary gravitational field of the solar system. Finally, proposals for future theoretical work being important for astrophysical applications are formulated.