Grounded hyperspheres as squashed wormholes

H. Alshal, Thomas Curtright

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Abstract

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.

Original languageEnglish (US)
Article number032901
JournalJournal of Mathematical Physics
Volume60
Issue number3
DOIs
StatePublished - Mar 1 2019

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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