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.
- Received 11 October 2002
DOI:https://doi.org/10.1103/PhysRevD.67.047501
©2003 American Physical Society