We compute exterior Green functions for equipotential, grounded hyperspheres in N-dimensional electrostatics by squashing Riemannian wormholes, where an image charge is placed in the branch of the wormhole opposite the branch containing the source charge, thereby providing a vivid geometrical approach to a method first suggested in 1897 by Sommerfeld. We compare and contrast the strength and location of the image charge in the wormhole approach with that of the conventional Euclidean solution where an image charge of reduced magnitude is located inside the hypersphere. While the two approaches give mathematically equivalent Green functions, we believe they provide strikingly different physics perspectives.
Cite
@article{arxiv.1806.03762,
title = {Grounded Hyperspheres as Squashed Wormholes},
author = {H Alshal and T Curtright},
journal= {arXiv preprint arXiv:1806.03762},
year = {2019}
}
Comments
Companion paper for arXiv:1805.11147 with minor typos corrected in version 2. To appear in J Math Phys