On the properties of the Ernst-Manko-Ruiz equatorially antisymmetric solutions

TL;DR

This paper analyzes two new equatorially antisymmetric solutions in general relativity, deriving explicit metric functions and examining conditions for equilibrium between counter-rotating objects, revealing specific parameter constraints for equilibrium.

Contribution

It provides explicit analytic forms of the metric functions for two new solutions and analyzes their equilibrium conditions, advancing understanding of antisymmetric gravitational configurations.

Findings

Two counter-rotating Kerr-Newman-NUT objects can be in equilibrium under a specific mass and charge condition.

Two equal masses with dipole moments cannot reach equilibrium, always requiring a strut.

Explicit metric functions are derived for both solutions.

Abstract

Two new equatorially antisymmetric solutions recently published by Ernst et al are studied. For both solutions the full set of metric functions is derived in explicit analytic form and the behavior of the solutions on the symmetry axis is analyzed. It is shown in particular that two counter-rotating equal Kerr-Newman-NUT objects will be in equilibrium when the condition m^2+\nu^2=q^2+b^2 is verified, whereas two counter-rotating equal masses endowed with arbitrary magnetic and electric dipole moments cannot reach equilibrium under any choice of the parameters, so that a massless strut between them will always be present.