Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

Assuming that the space-time is close to isotropic in the sense that the shear parameter is small and that the maximal velocity of the particles is bounded, we have been able to show that for non-diagonal Bianchi I-symmetric spacetimes with collisionless matter the asymptotic behaviour at late times is close to the special case of dust. We also have been able to show that all the Kasner exponents converge to 1/3 and an asymptotic expression for the induced metric has been obtained. The key was a bootstrap argument.Comment: V3 18 p. 3 fig. typos corrected, conclusions part extended, references added. To appear in Classical and Quantum Gravit

Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI0_0

In a recent paper arXiv:1208.4231 we have treated the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.Comment: 18 page

Polarized Electrogowdy spacetimes censored

A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstr\"{o}m on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.Comment: 6 pages, submitted to the conference proceedings of "Spanish relativity meeting 2009

The electromagnetic spike solutions

The aim of this paper is to use the existing relation between polarized electromagnetic Gowdy spacetimes and vacuum Gowdy spacetimes to find explicit solutions for electromagnetic spikes by a procedure which has been developed by one of the authors for gravitational spikes. We present new inhomogeneous solutions which we call the EME and MEM electromagnetic spike solutions.Comment: V3: 13 pages and 4 figures. No change in main result. Title and names of the solutions changed to make their physical interpretation more clea

Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein-Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein-Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.Comment: V3: 18 pages. Typos fixed. Matches published version. arXiv admin note: substantial text overlap with arXiv:1208.4231, arXiv:1208.615