Related papers: The Einstein-Vlasov system
A new Lagrangian framework has recently been proposed to describe interactions between relativistic perfect fluids and scalar fields. In this paper we investigate the Einstein static universe in this new class of theories, which have been…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
We study the Einstein-Lichnerowicz constraints system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
We study static spherically and hyperbolically symmetric solutions of the Einstein equations in the presence of a conformally coupled scalar field and compare them with those in the space filled with a minimally coupled scalar field. We…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
We prove well-posedness of the initial value problem for the Einstein equations for spatially-homogeneous cosmologies with data at an isotropic cosmological singularity, for which the matter content is either a cosmological constant with…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We investigate solutions of the $5$--dimensional rotating Einstein-Vlasov system with an $R \times SU(2) \times U(1)$ isometry group. In a five-dimensional spacetime, there are two independent planes of rotation, thus, considering $U(1)$…
By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations…
The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the…
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…
The classical unified theory of Weyl is revisited. The possibility of stable extended electron model in the Einstein-Weyl space is suggested.
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…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…