Pseudo-Newtonian Potential for Charged Particle in Kerr-Newman Geometry

TL;DR

This paper derives a pseudo-Newtonian potential for a charged particle in Kerr-Newman spacetime, providing a simplified classical model to approximate relativistic effects of charged particle motion around rotating charged black holes.

Contribution

It introduces a leading-order correction to the energy and angular momentum of charged particles in Kerr-Newman geometry and formulates a pseudo-Newtonian potential for easier analysis.

Findings

Derived conserved energy and angular momentum corrections for charged particles

Formulated a classical pseudo-Newtonian potential for Kerr-Newman black holes

Provided a simplified model to mimic relativistic charged particle dynamics

Abstract

We consider the equatorial circular motion of a test particle of specific charge q/m << 1 in the Kerr-Newman geometry of a rotating charged black hole. We find the particle's conserved energy and conserved projection of the angular momentum on the black hole's axis of rotation as corrections, in leading order of q/m, to the corresponding energy and angular momentum of a neutral particle. We determine the centripetal force acting on the test particle and, consequently, we find a classical pseudo-Newtonian potential with which one can mimic this general relativistic problem.