Homoclinic orbits in Kerr-Newman black holes

TL;DR

This paper derives exact analytical solutions for homoclinic orbits of particles in Kerr-Newman black holes, exploring their properties and effects of black hole charge and spin, with implications for astrophysical observations.

Contribution

It provides the first explicit analytical solutions for homoclinic orbits in Kerr-Newman spacetimes, including effects of black hole charge and spin.

Findings

Exact solutions expressed via elliptical integrals and Jacobi functions.

Parameter space analysis of homoclinic orbits.

Reduction to Kerr and zero angular momentum cases.

Abstract

We present the exact solutions of the homoclinic orbits for the timelike geodesics of the particle on the general nonequatorial orbits in the Kerr-Newman black holes. The homoclinic orbit is the separatrix between bound and plunging geodesics, a solution that asymptotes to an energetically bound, unstable spherical orbit. The solutions are written in terms of the elliptical integrals and the Jacobi elliptic functions of manifestly real functions of the Mino time where we focus on the effect from the charge of the black hole to the homoclinic orbits. The parameter space of the homoclinic solutions is explored. The nonequatorial homoclinic orbits in Kerr cases can be obtained by setting the charge of the black holes to be zero. The homoclinic orbits and the associated phase portrait as a function of the radial position and its derivation with respect to the Mino time are plotted using the analytical solutions. In particular, the solutions can reduce to the zero azimuthal angular moment homoclinic orbits for understanding the frame dragging effects from the spin as well as the charge of the black hole. The implications of the obtained results to observations are discussed.