A four--dimensional Neumann ovaloid
Complex Variables
2016-09-27 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
What is the shape of a uniformly massive object that generates a gravitational potential equivalent to that of two equal point-masses? If the weight of each point-mass is sufficiently small compared to the distance between the points then the answer is a pair of balls of equal radius, one centered at each of the two points, but otherwise it is a certain domain of revolution about the axis passing through the two points. The existence and uniqueness of such a domain is known, but an explicit parameterization is known only in the plane where the region is referred to as a Neumann oval. We construct a four-dimensional "Neumann ovaloid", solving explicitly this inverse potential problem.
Cite
@article{arxiv.1609.07702,
title = {A four--dimensional Neumann ovaloid},
author = {Lavi Karp and Erik Lundberg},
journal= {arXiv preprint arXiv:1609.07702},
year = {2016}
}
Comments
14 pages, 1 figure