Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis

TL;DR

This paper derives explicit formulas for key functions of the Neugebauer family of vacuum spacetimes based on axis data, facilitating understanding of their structure and enabling future extensions to more complex solutions.

Contribution

It provides a method to express the complex potential and metric functions of Neugebauer vacuum solutions from axis data, linking them to multipole moments and setting the stage for future generalizations.

Findings

Explicit formulas for E, omega, gamma in terms of axis data

Connection of axis data to multipole moments

Framework for extending to more transformations and electrovac solutions

Abstract

We express the complex potential E and the metrical fields omega and gamma of all stationary axisymmetric vacuum spacetimes that result from the application of two successive quadruple-Neugebauer (or two double-Harrison) transformations to Minkowski space in terms of data specified on the symmetry axis, which are in turn easily expressed in terms of multipole moments. Moreover, we suggest how, in future papers, we shall apply our approach to do the same thing for those vacuum solutions that arise from the application of more than two successive transformations, and for those electrovac solutions that have axis data similar to that of the vacuum solutions of the Neugebauer family. (References revised following response from referee.)