Stationary multiple euclidon solutions to the vacuum Einstein equations

TL;DR

This paper introduces a method for non-linear superposition of stationary euclidon solutions with axially symmetric gravitational fields, enabling the construction of many known vacuum solutions like Kerr-NUT with a new physical interpretation.

Contribution

It generalizes stationary soliton solutions to include arbitrary axially symmetric seed metrics using a simple, effective non-linear addition formula.

Findings

Constructed a superposition method for euclidon solutions

Enabled derivation of known solutions like Kerr-NUT

Provided a new physical interpretation as accelerated non-inertial frames

Abstract

The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the Einstein equations was generalized to the case of a stationary seed metric. The formulae obtained have a simple and compact form, permitting an effective non-linear "addition" of the solutions. These euclidon solutions serve as building block of the theory, which allows for the construction of almost all known solutions to the vacuum static axially-symmetric Einstein equations, including such important ones as the Kerr-NUT solution. The stationary euclidon solution has a clear physical interpretation as a relativistic accelerated non-inertial reference frame, which provides a different perspective on the physical interpretation of well-known solutions, such as the Kerr solution.