Optics of relativistic sources in a spherically symmetric gravitational field

The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)