Charged Radial Infall for Spherical Central Bodies

A massive, charged, spherical central body can be neutralized by attracting particles of opposite charge. We calculate the time it takes to neutralize these central bodies using classical mechanics, special relativistic mechanics, and finally, the “forced” trajectories of general relativity. While we can compare the classical and (special) relativistic times, and find, predictably, that the special relativistic neutralization time is longer, a comparison of these times with the general relativistic result is not as directly possible. We offer the final calculation as a demonstration of dynamics in a general setting and in particular, the structural similarity of the (general) relativistic problem to the other cases.