Motion of a charged test particle around a static black hole in a monopole magnetic field

Abstract

We study the motion of a charged test particle in the spacetime with a spherically symmetric black hole which is immersed in a monopole magnetic field. We show that the radial motion of the charged test particle is governed by completely the same equation as that in the case of no magnetic field. This result implies that the black hole will acquire the electric charge if it is surrounded by the collisionless plasma composed of protons and electrons which obey the Maxwell velocity distribution. The drastically different situation appears in the tangential motions of charged test particles due to the magnetic field. The trajectory of a charged test particle in the black hole with the magnetic field of the order of 10 Gauss near the black hole, is confined on a very thin cone as long as the specific angular momentum of the particle is not much larger than the gravitational radius of the black hole times the speed of light. This result leads to a possibility that a plasma lump can hover over the black hole and is very hot, in the monopole magnetic field.

Figures (4)

• Figure 1: A schematic diagram. Equation \ref{['allowed-domain']} is satisfied in the shaded region.
• Figure 2: A clump of plasma hovering on a black hole is depicted, where $\rho:=\sqrt{x^2+y^2}$. It occupies a domain $r_{\rm i}\leq r\leq r_{\rm i}+l$ and $0\leq\theta\leq\Theta$.
• Figure 3: The parameter region in which both Eq. \ref{['falling-condition-4']} and Eq. \ref{['falling-condition-5']} are satisfied as a shaded domain in the $(v_{(r)}^2$,${\cal K}^2)$-plane.
• Figure 4: A neighborhood of the surface at $x=0$ of a clump which occupies the domain $x<0$ is depicted. The centers of the circular orbits of particles are located in the domain $x\leq -l$. The velocities of particles located at $x$ are isotropic in the case of $x\leq -2l$, whereas those are anisotropic in the case of $-2l<x\leq0$.