Fully Electrified Neugebauer Spacetimes

TL;DR

This paper extends a method to explicitly express the complex potentials of all stationary axisymmetric electrovac spacetimes with specific axis data, linking parameters directly to multipole moments, thus broadening the understanding of these solutions.

Contribution

It generalizes a previous method to explicitly derive complex potentials for a broad class of electrovac spacetimes with specified axis data, connecting parameters to multipole moments.

Findings

Explicit formulas for complex potentials E and Phi in terms of parameters

Parameters directly related to multipole moments

Clarification of subtle points in the method

Abstract

Generalizing a method presented in an earlier paper, we express the complex potentials E and Phi of all stationary axisymmetric electrovac spacetimes that correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) , where U = z^{2} + U_{1} z + U_{2} , V = V_{1} z + V_{2} , W = W_{1} z + W_{2} , in terms of the complex parameters U_{1}, V_{1}, W_{1}, U_{2}, V_{2} and W_{2}, that are directly associated with the various multipole moments. (Revised to clarify certain subtle points.)