### 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 language | English (US) |
---|---|

Article number | 032901 |

Journal | Journal of Mathematical Physics |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*60*(3), [032901]. https://doi.org/10.1063/1.5044432

**Grounded hyperspheres as squashed wormholes.** / Alshal, H.; Curtright, Thomas.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 60, no. 3, 032901. https://doi.org/10.1063/1.5044432

}

TY - JOUR

T1 - Grounded hyperspheres as squashed wormholes

AU - Alshal, H.

AU - Curtright, Thomas

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063571023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063571023&partnerID=8YFLogxK

U2 - 10.1063/1.5044432

DO - 10.1063/1.5044432

M3 - Article

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

M1 - 032901

ER -