Title: Velocity dependence of point masses, moving on timelike geodesics, in weak gravitational fields,
Abstract: Applying the principle of equivalence, analogous to Einstein's original 1907
approach demonstrating the bending of light in a gravitational field, we deduce
that radial geodesics of point masses are velocity dependent. Then, using the
Schwarzschild solution for observers at spatial infinity, we analyze the
similar case of masses moving on timelike geodesics, rederiving a previous
result by Hilbert from 1917. We find that the Schwarzschild solution gives more
than twice the rate of falling than found from the simpler acceleration
arguments in flat space. We note Einstein also found a similar difference for
the bending of light between these two approaches and in this case the
increased deflection of light was due to space curvature. Similarly we find
that in our case, the discrepancy between the two approaches can be attributed
to space curvature. Although we have calculated the effect locally for
observers under a Schwarzschild coordinate system in a weak field, further work
needs to be carried out to explore the stronger field case.