New Euclidon Method of Generating Stationary Vacuum Einstein Fields

The purpose of this book is to systematically derive, as much as possible, the main exact asymptotically flat solutions of the static and stationary axially symmetric vacuum Einstein-Maxwell equations. The primary "building block" used is the Euclidon solution, which has a clear physical interpretation as a relativistic accelerated non-inertial reference frame in the flat space-time.In the first part, static Einstein fields are considered. The one-static Euclidon solution and its generalizations are obtained by various methods.The second part deals with the main classes of stationary vacuum Einstein field solutions. The one-stationary soliton solution, the one-stationary Euclidon solution, and its physical interpretation are obtained.In the third part, using the method of variation of parameters, solutions are obtained including a two-Euclidon stationary solution, which coincides with the Kerr-NUT solution.The fourth part deals with the main classes of static Einstein-Maxwell fields. The methods of superposition of the one-stationary Euclidon solution, the one-stationary soliton solution, and the two-Euclidon stationary solution with arbitrary external static electrovacuum fields are also applied to this case.The fifth part deals with stationary Einstein-Maxwell fields. The generalized solutions are constructed using symmetry transformations from the previously found solutions.