Equations of Motion of Schwarzschild, Reissner-Nordstrom and Kerr Particles

TL;DR

This paper introduces a method to derive the equations of motion for Schwarzschild, Reissner-Nordstrom, and Kerr particles in external fields, avoiding divergences and accounting for particle spin without treating them as test particles.

Contribution

It presents a new technique for extracting relativistic equations of motion from field equations, applicable to various black hole solutions, and derives the Mathisson-Papapetrou equations for spinning particles.

Findings

Method avoids divergent integrals in equations of motion

Derives equations for particles in Schwarzschild, Reissner-Nordstrom, Kerr backgrounds

Obtains spin equations neglecting spin-spin interactions

Abstract

A technique for extracting from the appropriate field equations the relativistic motion of Schwarzschild, Reissner-Nordstrom and Kerr particles moving in external fields is motivated and illustrated. The key assumptions are that (a) the particles are isolated and (b) near the particles the wave fronts of the radiation generated by their motion are smoothly deformed spheres. No divergent integrals arise in this approach. The particles are not test particles. The formalism is used, however, to derive the Mathisson-Papapetrou equations of motion of spinning test particles, neglecting spin-spin terms.