Papers
Authors
Leo Brewin
Abstract
As a test of the Regge calculus Williams and Ellis [1,2] computed, among
other quantities, the precession of the perihelia of Mercury.
Unfortunately they did not obtain anywhere near the correct values.
Their results varied between -2.74 and 0.42 radians per orbit. Their
best result was 9.1 x 10^{-4} radians per orbit whereas the correct
analytic value is 5.0 x 10^{-7} radians per orbit. A continuous time
version of their equations will be presented. It will be shown
numerically that, for a sufficiently fine discretization, the global
error between the Regge and Schwarzschild geodesics varies linearly with
the typical length scale for the Regge simplices. Some simple
modifications to the continuous time equations will then be presented.
It will be shown both numerically and analytically that the modified
equations yield paths that converge quadratically to the Schwarzschild
geodesics. The modified Regge equations will then be applied to the
problem of computing the precession of the perihelia of Mercury. The
result is a precession of 5.0 x 10^{-7} radians per orbit.