Electromagnetic self-force on a static charge in Schwarzschild–de Sitter spacetimes

Abstract

We compute the self-force acting on an electric charge at rest in Schwarzschild–de Sitter spacetimes, allowing the cosmological constant to be either positive or negative. In the case of a positive cosmological constant, we show that the self-force is always positive, representing a repulsion from the black hole, and monotonically decreasing with increasing distance from the black hole. The spectrum of results is richer in the case of a negative cosmological constant. Here, the self-force is not always positive—it is negative when the black-hole and cosmological scales are comparable and the charge is close to the black hole—and not always monotonically decreasing—it is actually monotonically increasing when the cosmological scale is sufficiently small compared to the black-hole scale. The self-force also approaches a constant asymptotic value when the charge is moved to large cosmological distances; this feature can be explained in terms of an interaction between the charge and the conformal boundary at infinity, which acts as a grounded conductor.