Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies

The Lorentz covariant theory of the propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving pointlike bodies with constant masses m₀ (a=1, 2, , N) is constructed. The theory is based on the Li\'enard-Wiechert representation of the metric tensor which describes a retarded type solution of the gravitational field equations. A new approach for integrating the equations of motion of light particles (photons) depending on the retarded time argument is invented. Its application in the first post-Minkowskian approximation, which is linear with respect to the universal gravitational constant G makes it evident that the equations of light propagation admit to be integrated straightforwardly by quadratures. Explicit expressions for the trajectory of a light ray and its tangent vector are obtained in algebraically closed form in terms of functionals of retarded time. General expressions for the relativistic time delay, the angle of light deflection, and the gravitational shift of electromagnetic frequency are derived in the form of instantaneous functions of retarded time. They generalize previously known results for the case of static or uniformly moving bodies. The most important applications of the theory to relativistic astrophysics and astrometry are given. They include a discussion of the velocity-dependent terms in the gravitational lens equation, the Shapiro time delay in binary pulsars, gravitational Doppler shift, and a precise theoretical formulation of the general relativistic algorithms of data processing of radio and optical astrometric measurements made in the nonstationary gravitational field of the solar system. Finally, proposals for future theoretical work being important for astrophysical applications are formulated.