Dynamics of Bianchi type I elastic spacetimes

Abstract

We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids. Based on our dynamical systems formulation of the equations we are able to prove that (i) toward the future all solutions isotropize; (ii) toward the initial singularity all solutions display oscillatory behavior; solutions do not converge to Kasner solutions but oscillate between different Kasner states. This behavior is associated with energy condition violation as the singularity is approached.

28 pages, 11 figures

References in corpus (6)

• Relativistic Elasticity
• The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies
• Relativistic elastodynamics
• The cosmological billiard attractor

Cited by in corpus (7)

• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• A new proof of the Bianchi type IX attractor theorem
• Cylindrically symmetric static solutions of the Einstein field equations for elastic matter
• Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process
• Relativistic elasticity of rigid rods and strings
• Rigid elastic solids in relativity
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models