Equilibrium of a charged spinning test particle in Reissner-Nordström backgrounds with a nonzero cosmological constant
The equilibrium of a charged test particle with spin located in the Reissner-Nordström background with a nonzero cosmological constant is investigated. The stationary equilibrium conditions resulting from the equations of motion and the equations of spin dynamics have to be satisfied simultaneously. It is shown that equilibrium conditions are independent of the spin of the test particle. For uncharged particles, they are satisfied at the so-called static radius, where gravitational attraction is exactly compensated for by cosmological repulsion. For charged particles, there is a variety of possible equilibria due to the electromagnetic interaction of the particle and the background. Any charged particle can be in an unstable equilibrium state between the black-hole and cosmological horizons of asymptotically de Sitter spacetimes, while sufficiently repulsed particles can be in an inner unstable equilibrium state and an outer stable equilibrium state above the horizon of asymptotically anti-de Sitter spacetimes. The separation-independent equilibrium is possible in extreme Reissner-Nordström spacetimes only.