Force on a static charge outside a Schwarzschild black hole

An exact calculation of the gravitationally induced electrostatic self-force on a charged test particle held stationary outside a Schwarzschild black hole is presented. After mass renormalization, there remains a finite repulsive force proportional to the square of the charge of the particle and to the mass of the black hole. In a local, freely falling frame momentarily at rest with respect to the charge, the repulsive force varies as the inverse cube of the Schwarzschild coordinate distance of the charge from the origin.