The quasi-Keplerian motion in the regular Bardeen spacetime

TL;DR

This paper derives a second post-Newtonian analytical solution for the quasi-Keplerian motion of a test particle around a regular Bardeen black hole, highlighting the effects of magnetic charge on orbital dynamics.

Contribution

It provides the first second post-Newtonian solution for particle motion in Bardeen spacetime, explicitly including magnetic charge effects on orbital parameters.

Findings

Magnetic charge influences perihelion precession.

Orbital period remains unaffected by magnetic charge at second post-Newtonian order.

Solution expressed in terms of energy, angular momentum, and black hole parameters.

Abstract

The second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the gravitational field of regular Bardeen black hole is derived. The solution is formulated in terms of the test particle's orbital energy and angular momentum, as well as the mass and magnetic charge of the Bardeen black hole. The leading effects of the magnetic charge on the test particle's orbit and motion including perihelion precession are displayed explicitly. In particular, it is shown that to the second post-Newtonian order the magnetic charge does not affect the test particle's orbital period.