The relations between the multipole moments in axistationary electrovacuum spacetimes and the $N$-soliton solution

TL;DR

This paper introduces a comprehensive analytical framework linking multipole moments to Ernst potentials in axistationary electrovac spacetimes, with applications demonstrating the practical utility of the formulation.

Contribution

It provides the first complete analytical description of how multipole moments determine Ernst potentials in axistationary electrovac spacetimes.

Findings

Closed-form expression for relativistic multipole moments.

Complete characterization of Ernst potentials via multipole moments.

Application examples illustrating the framework's utility.

Abstract

A general formulation of the relativistic multipole moments in axistationary electrovac spacetimes is introduced in a closed analytical form. We give a complete description of how the Ernst potentials on the symmetry axis can be completely characterized by these arbitrary multipole moments. Some concrete applications are also developed.