On the method of effective nonlinear sigma model in plane- and axially-symmetric vacuum spacetimes

Abstract

In present article effective nonlinear sigma model (NSM) is considered. Einstein equation solution, corresponded to the chiral fields determined by functional parameter method, are presented. Effective NSM of stationary axially-symmetric gravitational field is constructed. Motion equations are solved exactly by functional parameter method. Einstein equations solution are constructed. For particular dependences of functional parameter graphics of solutions are presented. Metric coefficients behaviour is shown to be similar as functional parameter one.