A Plane-Symmetric Gravitational Field as a Generalized Nonlinear Sigma Model

TL;DR

This paper reformulates Einstein's equations for a plane-symmetric gravitational field coupled with a nonlinear sigma model as a generalized effective NSM and finds exact solutions for a specific case using the functional parameter method.

Contribution

It introduces a generalized effective NSM framework for analyzing plane-symmetric gravitational fields coupled with nonlinear sigma models and derives exact solutions for a two-component diagonal case.

Findings

Reformulation of Einstein equations as a generalized NSM.

Derivation of exact solutions using the functional parameter method.

Analysis of gravitational equations through NSM methods.

Abstract

The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational equations are studied in this case by the methods of analyzing NSM equations. In the case of a two-component diagonal NSM exact solutions are found by the functional parameter method.