Charged Radial Infall for Spherical Central Bodies

TL;DR

This paper calculates the time required to neutralize charged spherical bodies using classical, special relativistic, and general relativistic mechanics, highlighting differences and structural similarities among these approaches.

Contribution

It provides a comparative analysis of neutralization times across classical, special relativistic, and general relativistic frameworks, illustrating the dynamics in each case.

Findings

Special relativistic neutralization time exceeds classical predictions.

General relativistic calculations demonstrate structural similarities to classical and relativistic cases.

The study highlights the complexity of dynamics in curved spacetime.

Abstract

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.