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

TL;DR

This paper calculates the electromagnetic self-force on a static charge in Schwarzschild-de Sitter spacetimes, revealing how the force varies with the cosmological constant and distance, including novel behaviors for negative cosmological constants.

Contribution

It provides the first detailed analysis of the self-force in Schwarzschild-de Sitter spacetimes with both positive and negative cosmological constants, highlighting new effects near the conformal boundary.

Findings

Self-force is positive and decreases with distance for positive cosmological constant.

Negative cosmological constant leads to non-monotonic and sign-changing self-force.

At large distances, the self-force approaches a constant due to boundary interactions.

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.