Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies - art. no. 124002

The Lorentz covariant theory of the propagation of light in the (weak) grav itational fields of N-body systems consisting of arbitrarily moving pointli ke bodies with constant masses m(a) (a = 1,2,...,N) is constructed. The the ory is based on the Lienard-Wiechert representation of the metric tensor wh ich 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 applica tion in the first post-Minkowskian approximation, which is linear with resp ect to the universal gravitational constant G makes it evident that the equ ations of light propagation admit to be integrated straightforwardly by qua dratures. Explicit expressions for the trajectory of a light ray and its ta ngent vector are obtained in algebraically closed form in terms of function als of retarded time. General expressions for the relativistic time delay, the angle of light deflection, and the gravitational shift of electromagnet ic frequency are derived in the form of instantaneous functions of retarded time. They,generalize previously known results for the case of static or u niformly moving bodies. The most important applications of the theory to re lativistic astrophysics and astrometry are given. They include a discussion of the velocity-dependent terms in the gravitational lens equation, the Sh apiro time delay in binary pulsars, gravitational Doppler shift, and a prec ise theoretical formulation of the general relativistic algorithms of data processing of radio and optical astrometric measurements made in the nonsta tionary gravitational field of the solar system. Finally, proposals for fut ure theoretical work being important for astrophysical applications are for mulated. [S0556-2821(99)07218-5].