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

TL;DR

This paper develops an effective nonlinear sigma model for stationary axially-symmetric vacuum spacetimes, providing exact solutions to Einstein's equations using the functional parameter method and analyzing their properties.

Contribution

It introduces a novel effective nonlinear sigma model approach and exact solution techniques for axially-symmetric vacuum spacetimes in general relativity.

Findings

Exact solutions to Einstein's equations are obtained.

Graphical analysis of metric coefficients is provided.

Behavior of solutions is shown to depend on the functional parameter.

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.