Self-force on a scalar charge in the spacetime of a stationary, axisymmetric black hole

We study the self-force acting on a particle endowed with scalar charge, which is held static (with respect to an undragged, static observer at infinity) outside a stationary, axially symmetric black hole. We find that the acceleration due to the self-force is in the same direction as the black hole’s spin, and diverges when the particle approaches the outer boundary of the black hole’s ergosphere. This acceleration diverges more rapidly approaching the ergosphere’s boundary than the particle’s acceleration in the absence of the self-force. At the leading order this self-force is a $(\mathrm{post}{)}^2$-Newtonian effect. For scalar charges with high charge-to-mass ratio, the acceleration due to the self-force starts dominating over the regular acceleration already far from the black hole. The self-force is proportional to the rate at which the black hole’s rotational energy is dissipated. This self-force is local (i.e., only the Abraham-Lorentz-Dirac force and the local coupling to Ricci curvature contribute to it). The non-local, tail part of the self-force is zero.