Null Geodesics in Perturbed Spacetimes

Mathematics – Logic

Scientific paper

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Gravitational Waves

Scientific paper

A method for constructing the geodesics of general metric perturbed space-times is presented and applied to three systems of astrophysical interest. First, the behavior of light scattering off a moving mass in Minkowski space is calculated and the result shown to agree with previously obtained formulae in the appropriate limits. Second, the method is used to provide a cosmological lens equation capable of expressing the effects of non-static, thick lenses on bundles of light rays. For thin, static lens systems, the general equation reduces to the standard cosmological lens equation, providing a rigorous derivation of the standard equation for those systems. Finally, Very Long Baseline Interferometry measurements in metric perturbed spacetimes are considered and an equation is written for the time delay measured by an antenna pair in an Einstein-de Sitter spacetime containing gravitational radiation.

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