Test particles in a magnetized conformastatic spacetime

TL;DR

This paper presents exact conformastatic solutions to Einstein-Maxwell equations, analyzing particle motion and orbital properties around a magnetic mass, with potential observational implications.

Contribution

It introduces a new class of solutions where gravitational and electromagnetic potentials are linked by a harmonic function, and explores particle dynamics in these spacetimes.

Findings

Charged particles can remain at rest due to electromagnetic forces.

Analytic expression for perihelion advance derived.

Spacetime describes a magnetic mass with specific orbital properties.

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. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function, which generates a singularity-free and asymptotically flat spacetime that describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles and the corresponding explicit value in the case of a punctual magnetic mass. We show that the analytical expressions obtained from our analysis are sufficient for being confronted with observations in order to establish whether such objects can exist in nature.