Motion of test particles in a magnetized conformastatic background

TL;DR

This paper explores the motion of test particles in a new class of exact, singularity-free conformastatic solutions of Einstein-Maxwell equations, revealing phenomena like repulsive forces and calculating perihelion advances.

Contribution

It introduces a novel class of exact conformastatic solutions where gravitational and electromagnetic potentials depend on a harmonic function, and analyzes test particle dynamics within this framework.

Findings

Existence of repulsive forces due to charge distribution.

Stable and unstable circular orbits identified.

Derived perihelion advance formula for these space-times.

Abstract

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is investigated in the background of a space-time characterized by this class of solutions. We focus on the study of circular stable and unstable orbits obtained by taking account particular harmonic functions defining the gravitational potential. We show that is possible to have repulsive force generated by the charge distribution of the source. As the space-time here considered is singularity free we conclude that this phenomena is not exclusive to the case of naked singularities. Additionally, we obtain an expression for the perihelion advance of the test particles in a general magnetized conformastatic space-time.