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Analytic description of singularities in Gowdy spacetimes
Satyanad Kichenassamy, Alan D. Rendall
We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary…
Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
Alan D. Rendall, Juan J. L. Velázquez
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of…
The spatially homogeneous relativistic Boltzmann equation with a hard potential
Ho Lee, Alan D. Rendall
In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner ine…
Construction of oscillatory singularities
Alan D. Rendall
One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic idea…
Oscillatory singularities in Bianchi models with magnetic fields
Stefan Liebscher, Alan D. Rendall, Sophonie Blaise Tchapnda
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approxima…
The Einstein-Boltzmann system and positivity
Ho Lee, Alan D. Rendall
The Einstein-Boltzmann system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momen…