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Electrostatic boundary value problems in the Schwarzschild background

Pal G. Molnar
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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--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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Pal G. Molnar. 2001-05-02. Electrostatic boundary value problems in the Schwarzschild background. https://doi.org/10.1088/0264-9381%2F18%2F10%2F304

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