Stationary Multiple Euclidon Solutions to the Vacuum Einstein Equations
In [1] 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. In the paper [1] stationary soliton solution of the Einstein equations was generalized to the case of a stationary seed metric. The formulae obtained in [1], [2] have a simple and compact form, permitting an effective non-linear ”addition” of the solutions. These euclidon solutions serve as ”building blocks” 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 [3].