Self-Force on a Particle in Orbit around a Black Hole

We study the self-force acting on a scalar charge in uniform circular motion around a Schwarzschild black hole. The analysis is based on a direct calculation of the self-force via mode decomposition, and on a regularization procedure based on Ori's mode-sum regularization prescription. We find the four self-forces at arbitrary radii and angular velocities (both geodesic and nongeodesic), in particular near the black hole, where general-relativistic effects are strongest, and for fast motion. We find the radial component of the self-force to be repulsive or attractive, depending on the orbit.