Soliton Nature of Equilibrium State of Two Charged Masses in General Relativity

TL;DR

This paper presents a new derivation of the equilibrium state for two charged masses in General Relativity, demonstrating its solitonic nature using the Inverse Scattering Method, and extending understanding of soliton solutions with electromagnetic fields.

Contribution

It introduces a solitonic derivation of the two-charged-masses equilibrium solution, linking it to a broader class of stationary axisymmetric electrovacuum solutions.

Findings

Solution is of solitonic character.

Supports the applicability of the Inverse Scattering Method with electromagnetic fields.

Shows the solution as a special case of a 12-parametric two-soliton solution.

Abstract

New derivation of static equilibrium state for two charged masses in General Relativity is given in the framework of the Inverse Scattering Method as an alternative to our previous derivation of this solution by the Integral Equation Method. This shows that such solution is of solitonic character and represents the particular case of more general (12-parametric) stationary axisymmetric electrovacuum two-soliton solution for two rotating charged objects obtained by one of the authors in 1986. This result gives an additional support to our comprehension that the appropriate analytical continuations of solitonic solutions in the space of their parameters are always possible and that applicability of the Inverse Scattering Method in presence of electromagnetic field is not restricted only to the cases with naked singularities.