Moment Density of Zipoy's Dipole Solution

TL;DR

This paper calculates the mass moment source for Zipoy's dipole solution in static axisymmetric gravitational fields, comparing it with Newtonian analogs, and employs techniques from magnetic and angular momentum density analyses.

Contribution

It introduces a method to compute the mass moment source for Zipoy's dipole solution using established techniques from related physical densities.

Findings

Derived the mass moment source for Zipoy's dipole solution.

Compared relativistic and Newtonian dipole analogs.

Enhanced understanding of gravitational field sources in axisymmetric solutions.

Abstract

Zipoy used spheroidal coordinates to construct a family of static axisymmetric gravitational fields included in Weyl's class. We calculate the mass moment source for the dipole solution using techniques previously developed for magnetic and angular momentum densities and compare it with the Newtonian analog studied by Bonnor and Sackfield.