Geodesic motion in a stationary dihole spacetime

Abstract

The knowledge of the properties of the different exact solutions modeling binary systems, is a necessary step towards the classification of physically suitable solutions and its corresponding limits of applicability. In the present paper, we perform an analysis of the geodesics around two counter-rotating Kerr-Newman black holes endowed with opposite electric charges, which achieve equilibrium by means of a strut between their constituents. We find that bounded and unbounded orbits are possible. However, test particles may cross between the black holes only if their angular momentum equals zero, otherwise, there exist a repulsive potential, which prohibits such orbits. Two important aspects are pointed out for these trajectories: (i) the motion of photons is affected once crossing the strut; and (ii) massive particles exhibit oscillatory motion, as a first analog of the Sitnikov problem in general relativity. The radius of the innermost stable circular orbit as a function of the physical parameters of the black holes is also investigated.

Energy extraction in electrostatic extreme binary black holes

“…It is worth mentioning that the motion equations for ρ and z, in terms of the metric (2) are given in [31] for neutral test particles. On the other hand, an explicit expression for the energy E is obtained by plugging the constants of motion (8) into the normalization condition of the four velocity ẋµ ẋµ = −1,…”

Geodesic dynamics in Chazy–Curzon spacetimes

“…Such potential can be derived as follows (see e.g. [26]): (i) From ( 1) and the relation 2L = g µν ẋµ ẋν , we get…”

A note on magnetic generalizations of the Kerr and Kerr–Newman solutions

“…In figures 2 and 3 the geodesic motion of massive test particles in the equatorial plane is depicted for three different types of orbits using formulae (7): a bounded orbit (figure 2), a regular circular orbit (figure 3(a)), and the path of a test particle moving under a small perturbation from the innermost stable circular orbit (ISCO) (figure 2(b); for the details of solving the geodesic equations the reader is referred to [28]). The particular choice of the parameters in (7) is the same for all these plots: m = 1, a = 0.4, q = 0.2, b = 0.25.…”