相关论文: The Einstein-Vlasov-Maxwell(EVM) System with Spher…

In this paper, we initiate the study of the asymptotically AdS initial-boundary value problem for the Einstein-massless Vlasov system with $\Lambda<0$ in spherical symmetry. We will establish the existence and uniqueness of a maximal future…

Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…

Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane…

Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the…

In this article the static Einstein-Vlasov-Maxwell system is considered in spherical symmetry. This system describes an ensemble of charged particles interacting by general relativistic gravity and Coulomb forces. First, a proof for local…

We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic…

We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…

We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution.…

It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…

The stability of static solutions of the spherically symmetric, asymptotically flat Einstein-Vlasov system is studied using a Hamiltonian approach based on energy-Casimir functionals. The main result is a coercivity estimate for the…

We investigate the Cauchy problem for the Einstein - scalar field equations in asymptotically flat spherically symmetric spacetimes, in the standard 1+3 formulation. We prove the local existence and uniqueness of solutions for initial data…

We show how to solve the Cauchy problem for the Einstein-Vlasov equations with geometric initial data on a light-cone.

New exact solution of the cylindrically symmetric Einstein-Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be…

Classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordstr\"{o}m-Vlasov system is its relation to the…

By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…

In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…

We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…

We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable $z$ (radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced…

The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological…

The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…