Taking the generality out of general relativity.

Statistics – Computation

Scientific paper

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Scientific paper

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. 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, the author's 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 or the Schwarzschild metric, and then performing algebraic simplications, 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.

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