Electrostatic boundary value problems in the Schwarzschild background

Details Electrostatic boundary value problems in the Schwarzschild background Electrostatic boundary value problems in the Schwarzschild background

2001-05-02

arxiv.org/abs/gr-qc/0105004v1

Class.Quant.Grav. 18 (2001) 1853-1869

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, no figures, uses iopart.sty

Scientific paper

10.1088/0264-9381/18/10/304

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--Nordstrom 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.

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