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.
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Research Article| September 01 1992
Space‐time geometries characterized by solutions to the geodesic equations
Keith Andrew, Charles G. Fleming; Space‐time geometries characterized by solutions to the geodesic equations. Comput. Phys. 1 September 1992; 6 (5): 498–505. https://doi.org/10.1063/1.168437
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