Related papers: Veiled singularities for the spherically symmetric…
We study an analytical solution to the Einstein's equations in 2+1-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this…
Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly…
We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such…
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
All the classes of static massless scalar field models available currently in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields…
In this paper, we study the instability of naked singularities arising in the Einstein equations coupled with isothermal perfect fluid. We show that the spherically symmetric self-similar naked singularities of this system, are unstable to…
We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major…
The problem of constructing naked singularities in general relativity can be naturally divided into two parts: (i) the construction of the region exterior to the past light cone of the singularity, extending all the way to (an incomplete)…
In the previous works [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478 and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum…
We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are…
Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.
We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature…
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$…
In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in $n$ dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat…
We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary…
The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We…