Abstract. The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution. Boundary value problems are solved. With a multipole expansion the asymptotic property for the field of any charge distribution is derived. It is shown that one produces a Reissner-Nordström black hole if one lowers a test charge distribution slowly toward the horizon. The symmetry of the distribution is not important. All the multipole moments fade away except the monopole. A calculation of the gravitationally induced electrostatic self-force on a pointlike test charge distribution held stationary outside the black hole is presented.

PACS numbers: 0240K, 0440N, 0470B, 4120C

Print publication: Issue 10 (21 May 2001)
Received 15 August 2000, in final form 12 March 2001