Inspiral and Plunging Orbits in Kerr-Newman Spacetimes

TL;DR

This paper derives explicit analytical solutions for the trajectories of particles spiraling and plunging into Kerr-Newman black holes along non-equatorial paths, with potential implications for gravitational wave studies.

Contribution

It provides the first comprehensive analytical solutions for non-equatorial particle orbits in Kerr-Newman spacetimes, extending previous equatorial-only results.

Findings

Solutions expressed via elliptical integrals and Jacobian elliptic functions.

Reduces to known solutions for Kerr, Reissner-Nordström, and Schwarzschild black holes.

Potential applications in modeling gravitational wave emissions from extreme mass-ratio inspirals.

Abstract

We present the analytical solutions for the trajectories of particles that spiral and plunge inward the event horizon along the timelike geodesics following general non-equatorial paths within Kerr-Newman spacetimes. Our studies encompass both bound and unbound motions. The solutions can be written in terms of the elliptical integrals and the Jacobian elliptic functions of manifestly real functions of the Mino time. They can respectively reduce to the Kerr, Reissner-Nordstr$\ddot{o}$m, and Schwarzschild black holes in certain limits of the spin and charge of the black holes, and can be compared with the known ones restricted in equatorial motion. These explicit solutions may have some implications for the gravitational wave emission from extreme mass-ratio inspirals.