Stationary Multiple Euclidon Solutions to the Vacuum Einstein Equations

This paper is dedicated to Professor Ts.I. Gutsunaev, who recently passed away. In our previous paper [1] we constructed a nonlinear superposition of a stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field using the method of variation of parameters. In the same work [1], a stationary soliton solution to the Einstein equations was generalized to the case of a stationary seed metric. The formulas obtained in [1, 2] have a simple, compact structure that enables an effective non-linear “addition” of solutions. In this framework, euclidon solutions serve as building blocks that generate almost all known vacuum, static, axially symmetric solutions to the Einstein equations, including the important Kerr–NUT family. Moreover, the stationary euclidon solution admits a clear physical interpretation as a relativistically accelerated, noninertial reference frame, providing an alternative perspective on the physical meaning of celebrated solutions such as Kerr’s [3].