Corpus ID: 141478079

Green Functions, Sommerfeld Images, and Wormholes

@article{Alshal2019GreenFS,
  title={Green Functions, Sommerfeld Images, and Wormholes},
  author={Hassan Alshal},
  journal={arXiv: Classical Physics},
  year={2019}
}
Electrostatic Green functions for grounded equipotential circular and elliptical rings, and grounded hyperspheres in n-dimension electrostatics, are constructed using Sommerfeld’s method. These electrostatic systems are treated geometrically as different radial p-norm wormhole metrics that are deformed to be the Manhattan norm, namely “squashed wormholes”. Differential geometry techniques are discussed to show how Riemannian geometry plays a role in Sommerfeld’s method. A comparison is made in… Expand

References

SHOWING 1-10 OF 22 REFERENCES
The Conducting Ring Viewed as a Wormhole
We compute the exterior Green function for a grounded equi-potential circular ring in two-dimensional electrostatics by treating the system geometrically as a "squashed wormhole" with an image chargeExpand
Grounded hyperspheres as squashed wormholes
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 theExpand
Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity
Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novelExpand
Solution to Potential Problems near a Conducting Semi-Infinite Sheet or Conducting Disk
An image technique (due to Sommerfeld) that is appropriate for finding the potential of an electrical charge near a conducting semi-infinite sheet is reviewed. The technique is extended to aExpand
Some properties of hyperspherical harmonics
A general formula is given for the canonical decomposition of a homogeneous polynomial of order λ in m variables into a sum of harmonic polynomials. This formula, which involves successiveExpand
Ellipsoidal Harmonics: Theory and Applications
Prologue 1. The ellipsoidal system and its geometry 2. Differential operators in ellipsoidal geometry 3. Lame functions 4. Ellipsoidal harmonics 5. The theory of Niven and Cartesian harmonics 6.Expand
Ether flow through a drainhole - a particle model in general relativity
The Schwarzchild manifold of general relativitytheory is unsatisfactory as a particle model because the singularity at the origin makes it geodesically incomplete. A coupling of the geometry ofExpand
Image Charges Re-Imagined.
We discuss the grounded, equipotential ellipse in two-dimensional electrostatics to illustrate different ways of extending the domain of the potential and placing image charges such that homogeneousExpand
The Particle Problem in the General Theory of Relativity
The writers investigate the possibility of an atomistic theory of matter and electricity which, while excluding singularities of the field, makes use of no other variables than the g&„of the generalExpand
Visualizing Interstellar's Wormhole
Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities,Expand
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