Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime

TL;DR

This paper derives exact solutions for the Einstein-Skyrme model within a Kantowski-Sachs spacetime, utilizing Lie symmetries and Noether's theorem to analyze the wavefunction and cosmological parameters.

Contribution

It introduces a novel approach to solving the Einstein-Skyrme model by applying symmetry analysis and conservation laws to the Wheeler-DeWitt equation in a Kantowski-Sachs background.

Findings

Invariant solutions for the wavefunction are obtained.

Conservation laws for the field equations are constructed.

Cosmological parameters are expressed in terms of the scale factor.

Abstract

We consider a Skyrme fluid with a constant radial profile in locally rotational Kantowski-Sachs spacetime. The Skyrme fluid is an anisotropic fluid with zero heat flux and with an equation of state parameter $w_{S}$ that $\left\vert w_{s}\right\vert \leq\frac{1}{3}$. From the Einstein field equations we define the Wheeler-DeWitt equation. For the last equation we perform a Lie symmetry classification and we determine the invariant solutions for the wavefunction of the model. Moreover from the Lie symmetries of the Wheeler-DeWitt equation we construct Noetherian conservation laws for the field equations which we use in order to write the solution in closed form. We show that all pf the cosmological parameters are expressed in terms of the scale factor of the two dimensional sphere of the Kantowski-Sachs spacetime. Finally from the application of Noether's theorem for the Wheeler-DeWitt equation we derive conservation laws for the wavefunction of the universe.