Perfect fluids and generic spacelike singularities

We present the conformally 1+3 Hubble-normalized field equations together with the general total source equations, and then specialize to a source that consists of perfect fluids with general barotropic equations of state. Motivating, formulating, and assuming certain conjectures, we derive results about how the properties of fluids (equations of state, momenta, angular momenta) and generic spacelike singularities affect each other.Comment: Considerable changes have been made in presentation and arguments, resulting in sharper conclusion

Dynamics of Bianchi type I elastic spacetimes

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.Comment: 28 pages, 11 figure

Monotonic functions in Bianchi models: Why they exist and how to find them

All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio

New explicit spike solution -- non-local component of the generalized Mixmaster attractor

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate non-colour printin

Bianchi type I models with two tilted fluids

In this paper we investigate expanding Bianchi type I models with two tilted fluids with linear equations of state. Individually the fluids have non-zero energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because of the Codazzi constraint. Asymptotically toward the past the solutions approach Kasner states if the speeds of sound are less than that of light. If one of the fluids has a speed of sound that is less or equal to 1/3 of the speed of light (radiation) then the models isotropize toward the future, but if both fluids are stiffer than radiation then the final state is anisotropic with non-zero Hubble-normalized shear. The significance of these results is discussed in a broader context.Comment: 19 pages, 2 figure