Equilibrium conditions of spinning test particles in Kerr–de Sitter spacetimes

Abstract

Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant cases of equilibrium positions in the equatorial plane and on the symmetry axis of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes. In the equatorial plane, it is possible at the so-called static radius, where the gravitational attraction is balanced by the cosmic repulsion, for the spinless particles as well as for spinning particles with arbitrarily large ϕ-oriented spin or at any radius outside the ergosphere with a specifically given spin orthogonal to the equatorial plane. On the symmetry axis, the equilibrium is possible at any radius in the stationary region and is given by an appropriately tuned spin directed along the axis. At the static radii on the axis the spin of particles in equilibrium must vanish.

Quasi-Maxwell interpretation of the spin–curvature coupling

“…(5) will be exact for the Mathisson-Pirani supplementary condition if the angular momentum is aligned with the "Poynting vector" G ×H. Thus for instance the equilibrium positions along the axis of the Kerr-de Sitter solution, computed in [28] using the Mathisson-Pirani supplementary condition, coincide with the equilibrium positions computed using TulczyjewDixon supplementary condition, and can both be obtained from (5).…”

Current-carrying string loops in black-hole spacetimes with a repulsive cosmological constant

“…In the spacetimes with the repulsive cosmological term, motion of photons is treated in a series of papers [15][16][17][18][19][20][21][22][23], while motion of test particles and perfect fluid was studied in [5,[24][25][26][27][28][29][30]. Equilibrium positions of spinning test particles were investigated in [31][32][33][34]. The cosmological constant can be relevant in both the geometrically thin [9,10,24,35,36] and thick accretion discs [37][38][39][40][41] orbiting around supermassive black holes in the center of giant galaxies.…”

Spinning test particles in the γ spacetime

“…-for details, see [11]. Similarly, the characteristic orbits of spinning particles in non-rotating and rotating axially symmetric space-times, are shifted inward or outward depending on signature of the spin of the particle, with respect to the non-spinning case [20][21][22][23][24][25][26][27][28][29][30][31][32].…”