Off-equatorial orbits in strong gravitational fields near compact objects

Abstract

Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We study a possibility that the interplay between gravitational and electromagnetic action may allow for stable, energetically bound off-equatorial motion of charged particles. This would represent well-known generalized Störmer's 'halo orbits', which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of Kerr-Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.

Inducing Chaos by Breaking Axial Symmetry in a Black Hole Magnetosphere

“…Since α > 0 above the horizon the motion is allowed just if E V eff . A method of effective potential has been applied to locate confinements (both equatorial and off-equatorial) of charged matter in several stationary and axisymmetric models in our previous works (Kovář et al 2008(Kovář et al , 2010Kopáček et al 2010a). The potential V eff was investigated as a function of two configuration variables r and θ , angular momentum L, and particular parameters of the given system.…”

“…As a first step, the existence of off-equatorial orbits was investigated in the spacetime described by the exact Kerr-Newman solution, i.e., the case of a rotating, electrically charged black hole. Considering only the astrophysically relevant region above the outer horizon of the black hole, it was found that there are no stable circular orbits (halo orbits) outside the equatorial plane (Kovář et al 2008). Therefore, we altered our model, namely, we employed test field solutions describing large-scale, ordered magnetic fields (asymptotically uniform or dipole type) in which the compact object is immersed.…”

Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field

“…Existence of the off-equatorial circular motion of charged particles in the combined electromagnetic and gravitational fields has been considered in [34][35][36]. Possible existence of the off-equatorial levitating toroidal configurations has been also demonstrated in [37].…”

Off-equatorial circular orbits in magnetic fields of compact objects

“…In the last case, the solution was found by de Felice (1979) and Calvani et al (1982). But the authors only simply conclude that the halo orbits do exist in Kerr-Newman spacetimes, regardless of the stability of the orbits and Kerr-Newman black-hole and naked-singularity space-time classes.Our study (see the paper Kovář et al (2008)) points out the stable halo orbits existence near all of the three studied kinds of compact objects. However, in the case of KerrNewman black hole, the stable halo orbits are of marginal astrophysical importance, being hidden under the inner event horizon.…”