Moment density of Zipoy's dipole solution

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.

Generating Black Strings in Higher Dimensions

“…Let us consider the ZV solution [9] in Weyl coordinates (for a discussion on Zipoy-Voorhees solution see [10]), with the line element (2) and the metric functions given by:…”

Non-regular Potentials and Sources for Static Axisymmetric Electrovacs

“…After the fashion of [3], [6], [7], an asymptotically cartesian function Z will be introduced and will be taken to satisfy the same differential equation as V :…”

Geodesic completeness of orthogonally transitive cylindrical space–times

“…Since all known diagonal cylindrical perfect fluid models ( [11], [12], [13], [14]) with regular curvature invariants have already been shown to be geodesically complete [4], we shall only concern about nondiagonal ones. To our knowledge there are just two and both can be derived from Einstein spacetimes using the Wainwright-Ince-Marshman generation algorithm for stiff perfect fluids [15].…”

“…[1], [2] and references therein) in order to determine whether a spacetime is singular. But on the contrary theorems that provide large families of nonsingular spacetimes are not very usual [3], [4] and in principle the proof of geodesic completeness involves cumbersome calculations [5].…”

“…Our aim will be the generalization of the theorem on diagonal orthogonally transitive cylindrical spacetimes in [4] to nondiagonal models and thereby comprise all known nonsingular cylindrical perfect fluid spacetimes in the literature.…”