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

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 $\left|w_s\right|\le \frac{1}{3}$. 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.

arXiv comment13 pages, 3 figures

References in corpus (26)

• Noether Symmetry in $f(T)$ Theory
• Some Anisotropic Dark Energy Models in Bianchi Type-V Space-time
• Dynamical analysis in scalar field cosmology
• Constraints and analytical solutions of $f(R)$ theories of gravity using Noether symmetries
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Noether symmetric $f(R)$ quantum cosmology and its classical correlations
• Non-linear superposition law and Skyrme crystals
• An introduction to quantum cosmology
• Skyrmions and Semilocal Strings in Cosmology
• Spinning Gravitating Skyrmions
• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• FLRW metric $f(R)$ cosmology with a perfect fluid by generating integrals of motion
• Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities
• Noether analysis of Scalar-Tensor Cosmology
• Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
• Quantum Cosmology of Kantowski-Sachs like Models
• Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries
• Introductory Lectures on Quantum Cosmology (1990)
• Kantowski-Sachs Universes sourced by a Skyrme fluid
• Expanding Spherically Symmetric Models without Shear
• Wheeler-DeWitt quantization and singularities
• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
• Noether and Lie symmetries for charged perfect fluids
• Cosmological dynamics of gravitating hadron matter
• Symmetries of homogeneous cosmologies
• A fifth order differential equation for charged perfect fluids

Cited by in corpus (5)

• Cosmological Einstein-Skyrme solutions with non-vanishing topological charge
• Dynamical system analysis of Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• Kantowski-Sachs cosmology in scalar-torsion theory
• Cosmic Inflation From Fluctuating Baby-Skyrme Brane