Dynamics of Quiet Universes

Abstract

We study the stability of a contracting {\it silent universe}, which is a spacetime with irrotational dust and vanishing magnetic part of the Weyl tensor, $H_{ab}=0$. Two general relativistic backgrounds are analyzed; one is an attractor of {\it silent universes}, i.e., a locally Kasner spacetime, and the other is a particular class of inhomogeneous Szekeres solutions. In both cases their stabilities against perturbations with non-zero magnetic part depend on a contraction configuration; a spindle-like collapse is unstable, while a pancake-like collapse is still stable. We also find that a similar instability exists in spindle collapse for a Newtonian case. We conclude that $H_{ab}=0$ is not a generic ansatz even in general relativistic dust collapse.

21 pages, 8 eps figures

References in corpus (6)

• General Relativistic Dynamics of Irrotational Dust: Cosmological Implications
• Dynamics of Silent Universes
• Lagrangian Evolution of the Weyl Tensor
• Gravitational Instability of Cold Matter
• A Local View of the Observable Universe
• Integrability Conditions for Irrotational Dust with a Purely Electric Weyl Tensor: A Tetrad Analysis

Cited by in corpus (7)

• Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes
• A prediction for anisotropies in the nearby Hubble flow
• Symmetries and Singularities of the Szekeres System
• Quantization of the Szekeres System
• Gauss-Bonnet-Chern approach to the averaged Universe
• The Quasi-Maxwellian Equations of General Relativity: Applications to the Perturbation Theory
• Equilibrium configurations in the dynamics of irrotational dust matter