Space-time geometries characterized by solutions to the geodesic equations

A novel method for calculating and visualizing the geodesic structure of space-time models is presented. By utilizing the symbolic computational power of Mathematica on a NeXT, and an IBM RS 6000 workstation, the geodesic equations are found analytically for any given metric. Once spliced into a fortran program, the geodesic equations are solved numerically, on a CRAY Y-MP supercomputer, for a given bundle of null geodesics. Here, the null geodesic structure of three singular space-time geometries is examined: the Schwarzchild, Kerr, and Winicour space-times. Using Mathematica software, the numerical data for the geodesic paths is displayed graphically, providing a picture of a given spacetime volume for each set of initial conditions. The parameter dependence of space-time, due to a particular metric, can be observed by sequencing through various parameters, such as the mass and spin. These pictures can then be composed into a video tape which displays the range of behavior as the parameters are varied.