Pál G Molnár 2001 Class. Quantum Grav. 18 1853 doi:10.1088/0264-9381/18/10/304
Pál G Molnár
Show affiliationsThe 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.
04.70.-s Physics of black holes
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
Issue 10 (21 May 2001)
Received 15 August 2000, in final form 12 March 2001
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