Interaction of Hawking radiation and a static electric charge

We investigate whether the equality found for the response of static scalar sources interacting (i) with Hawking radiation in Schwarzschild spacetime and (ii) with the Fulling-Davies-Unruh thermal bath in the Rindler wedge is maintained in the case of electric charges. We find a finite result in the Schwarzschild case, which is computed exactly, in contrast with the divergent result associated with the infrared catastrophe in the Rindler case, i.e., in the case of uniformly accelerated charges in Minkowski spacetime. Thus the equality found for scalar sources does not hold for electric charges.