Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector

TL;DR

This paper investigates the integrability of a specific Einstein-nonlinear $SU(2)$ sigma-model with a nonzero cosmological charge, demonstrating that the gravitational equations are integrable through singularity analysis.

Contribution

It applies singularity analysis to establish the integrability of the Einstein-nonlinear $SU(2)$ sigma-model with nonvanishing cosmological charge.

Findings

Gravitational field equations are integrable.

Solutions are obtainable via singularity analysis.

First terms of solutions are explicitly presented.

Abstract

The integrability of the\ $\Lambda-$Einstein-nonlinear $SU(2)$ $\sigma$-model with nonvanishing cosmological charge is studied. We apply the method of singularity analysis of differential equations and we show that the equations for the gravitational field are integrable. The first few terms of the solution are presented.