Related papers: Homoclinic orbits in Kerr-Newman black holes
Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition. For equatorial Kerr orbits,…
In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling. As a companion to that physical space study, in this paper we paint a phase…
We study the null and time-like geodesics of the light and the neutral particles respectively in the exterior of Kerr-Newman black holes. The geodesic equations are known to be written as a set of first-order differential equations in Mino…
We present a family of analytic solutions for the nearly-equatorial motion of a test particle with precessing spin in Kerr spacetime. We solve the equations of motion up to linear order in the small body's spin for periodic and homoclinic…
Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned,…
We study the order ten polynomial equation satisfied by the radius of the spherical timelike orbits for a massive particle with a generic energy around a Kerr black hole. Even though the radii of the prograde and retrograde orbits at the…
We provide an exhaustive and illustrated classification of timelike and null geodesics in the near-horizon region of near-extremal Kerr black holes. The classification of polar motion extends to Kerr black holes of arbitrary spin. The…
We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy…
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…
The motion of a spinning particle in the exterior of a Kerr-Newman black hole is studied. The dynamics is governed by the Mathisson-Papapetrou equations in the pole-dipole approximation, including the spin-curvature coupling to leading…
The Kerr separatrix is a boundary in parameter space that separates bound orbits from plunging orbits in the Kerr black hole space-time. Recently, Stein and Warburton found a polynomial equation for the location of the separatrix, for two…
The Hamilton-Jacobi equation for test particles in the Kerr geometry is separable. Using action-angle variables, we establish several relations between various physical quantities that characterize bound timelike geodesic orbits around a…
We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $\lambda$ as the independent variable. Mino time decouples…
In this paper, we continue our study of the motion of spinning test bodies orbiting Kerr black holes. Non-spinning test bodies follow geodesics of the spacetime in which they move. A test body's spin couples to the curvature of that…
We study the geodesic equations in the space-time of neutral Brans-Dicke Dilaton black hole in three dimensions, BTZ black holes and the 2+1 black hole. We use the process of separation of the Hamilton-Jacobi equation to obtain the…
The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature…
We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of…
We study the orbits of a spinning particle in the Reissner-Nordstr\"om black hole exterior through the spin-curvature coupling to leading order in its spin. The dynamics is governed by the Mathisson-Papapetrou equations in the pole-dipole…
A small deformation controlled by four free parameters to the Schwarzschild metric could be referred to a nonspinning black hole solution in alternative theories of gravity. Because such a non-Schwarzschild metric can be changed into a…
The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the…