Phys. Rev. D 67, 047501 (2003) [3 pages]Uniqueness of the electrostatic solution in Schwarzschild spaceReceived 11 October 2002; published 27 February 2003 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. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.67.047501
DOI:
10.1103/PhysRevD.67.047501
PACS:
04.40.Nr, 02.40.Ky, 41.20.Cv
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