Inspiral and Plunging Orbits in Kerr-Newman Spacetimes

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.