Ernesto Nungesser

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

Assuming that the spacetime 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 and an asymptotic expression for the induced metric has been obtained. The key was a bootstrap argument.The sign conventions of [18] are used. In particular, we use a metric signature − + + + and geometrized units, i.e. the gravitational constant G and the speed of light c are set equal to 1. Also the Einstein summation convention that repeated indices are to be summed over is used. Latin indices run from 1 to 3. C will be an arbitrary constant and will denote a small and strictly positive constant. They both may appear several times in different equations or inequalities without being the same constant. A dot above a letter will denote a derivative with respect to the cosmological (Gaussian) time t.

Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI0

In a recent paper [E. Nungesser, “Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0,” Annales Henri Poincare (2012)10.1007/s00023-012-0201-0], we have treated the future nonlinear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. 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.

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.

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.

Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.

Late-time behaviour of the Einstein–Boltzmann system with a positive cosmological constant

In this paper we study the Einstein-Boltzmann system for Israel particles with a positive cosmological constant. We consider spatially homogeneous solutions of Bianchi types except IX and obtain future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system. The result shows that the solutions converge to the de Sitter solution at late times.

Self-Similarity Breaking of Cosmological Solutions with Collisionless Matter

In this paper we consider the Einstein–Vlasov system with Bianchi VII

Future non-linear stability of the Einstein-Vlasov system with reflection Bianchi II and VI0 symmetry

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