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.
Highlights
The purpose of this work is to study the integrability of the field equations of the Einstein-nonlinear SU (2) σ -model, which have been studied previously in [4]
The application of singularity analysis in gravitational theories has been applied by many researchers in the past, for instance in the case of the mixmaster universe (Bianchi IX)
The physical implication of the action, (2), is that it describes the dynamics of low energy pions
Summary
The purpose of this work is to study the integrability of the field equations of the Einstein-nonlinear SU (2) σ -model, which have been studied previously in [4]. The action integral of the field equations for the Einstein-nonlinear SU (2) σ -model in a fourdimensional manifold is given by U −1U;μ gμν U −1U;ν where U (xν) is the SU (2)-valued scalar and K is a positive constant.
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