Equilibrium of a charged test particle in the Kerr - Newman spacetime: force analysis

104

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.

“…Projecting the right-hand side of the Lorentz equation (A.4), we obtain the equation [19] qh i j F ik u k = E j + M j , (A. 13) where E j = qγF jk n j , (A.14)…”

Section: Discussionmentioning

confidence: 99%

Off-equatorial orbits in strong gravitational fields near compact objects

Kovář¹,

Stuchlík²,

Karas³

2008

104

“…For the uniform and axially symmetric rotation (32), the centrifugal force formula (56) reduces to formula (27). The embedding diagram ofΣ t equatorial plane is governed by the general embedding formula (51). Here, taking its particular form…”

Section: Conformal Transformation C = E −φmentioning

confidence: 99%

Charged fluids encircling compact objects: force representations and conformal geometries

Kovář¹,

Kojima²,

Slaný³

et al. 2020

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy-momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy-momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

“…Thus, we arrive to covariant definition of inertial forces analogous to the Newtonian physics [2,17] …”

Section: General Casementioning

confidence: 99%

Optical reference geometry of Kerr-Newman spacetimes

Stuchlík

Hledík

Juran

2000

Abstract. Properties of the optical reference geometry related to Kerr-Newman black-hole and naked-singularity spacetimes are illustrated using embedding diagrams of their equatorial plane. It is shown that among all inertial forces defined in the framework of the optical geometry, just the centrifugal force plays a fundamental role in connection to the embedding diagrams because it changes sign at the turning points of the diagrams. The embedding diagrams do not cover the stationary part of the Kerr-Newman spacetimes completely. Hence, the limits of embeddability are given, and it is established which of the photon circular orbits hosted the by Kerr-Newman spacetimes appear in the embeddable regions. Some typical embedding diagrams are constructed, and the Kerr-Newman backgrounds are classified according to the number of embeddable regions of the optical geometry as well as the number of their turning points. It is shown that embedding diagrams are closely related to the notion of the radius of gyration which is useful for analyzing fluid rotating in strong gravitational fields.