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Uniqueness of the electrostatic solution in Schwarzschild space

Pal G. Molnar·Klaus Elsasser
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Abstract

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.

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Pal G. Molnar, Klaus Elsasser. 2003-03-02. Uniqueness of the electrostatic solution in Schwarzschild space. https://doi.org/10.1103/physrevd.67.047501

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