On the Einstein-Vlasov system with hyperbolic symmetry

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discusse

Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a scalar field, subject to the Vlasov and wave equations respectively. The spacetime is future geodesically complete in the special case of plane symmetry with only a scalar field. Causal geodesics are also shown to be future complete for homogeneous solutions of the Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page

Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.Comment: 12 page

Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.Comment: 2

A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (i.e., discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein-Euler equations.Comment: 24 page

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated

Late-time oscillatory behaviour for self-gravitating scalar fields

This paper investigates the late-time behaviour of certain cosmological models where oscillations play an essential role. Rigorous results are proved on the asymptotics of homogeneous and isotropic spacetimes with a linear massive scalar field as source. Various generalizations are obtained for nonlinear massive scalar fields, $k$-essence models and $f(R)$ gravity. The effect of adding ordinary matter is discussed as is the case of nonlinear scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference

Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states of the spacetimes near the singularity or in a phase of unlimited expansion. Bianchi type II models show oscillatory behaviour near the initial singularity which is, however, simpler than that of the mixmaster model.Comment: 27 pages, 3 figures, LaTe