Motions and world-line deviations in Einstein-Maxwell theory

TL;DR

This paper investigates the motion and deviations of charged particles in Einstein-Maxwell backgrounds, focusing on pp-waves and Reissner-Nordström solutions, and verifies results through analytical checks.

Contribution

It introduces a detailed analysis of world-line deviations for charged particles in specific Einstein-Maxwell backgrounds, including new calculations and consistency checks.

Findings

Derived deviation equations for charged particles in Einstein-Maxwell fields

Analyzed particle motion in pp-wave and Reissner-Nordström backgrounds

Confirmed consistency of deviation approach with direct geodesic calculations

Abstract

We examine the motion of charged particles in gravitational and electro-magnetic background fields. We study in particular the deviation of world lines, describing the relative acceleration between particles on different space-time trajectories. Two special cases of background fields are considered in detail: (a) pp-waves, a combination of gravitational and electro-magnetic polarized plane waves travelling in the same direction; (b) the Reissner-Nordstr{\o}m solution. We perform a non-trivial check by computing the precession of the periastron for a charged particle in the Reissner-Nordstr{\o}m geometry both directly by solving the geodesic equation, and using the world-line deviation equation. The results agree to the order of approximation considered.