Taking the generality out of general relativity

Although much has been written about relativity, little delves into its actual equations. Even rarer does one find relativity used in any sort of computation, such as one would find in a computer simulation. This is sad. it is hoped to be shown here not just the problems one might encounter in writing such a simulation, but also that one can perform a simulation of general relativity without too much effort. In fact, our experience has been that a program simulating geodesic motion in general relativity requires no more lines of code than a corresponding program to simulate planetary motion using Newton's laws. The relativity program is straightforward and general, but slow. However, by mechanically substituting the equations for the gravitational time-dilation metric of the Schwarzchild metric, and then performing algebraic simplifications, one can obtain a program whose simulation time is as fast as a corresponding Newtonian motion simulation. The resulting customized relativity programs are again short and simple. Customization does, however, obscure a little relation between the general equations and those actually used.