Related papers: Naked singularities in the Einstein-Euler system
In this paper, we study solutions to the Klein-Gordon equation on Bianchi backgrounds. In particular, we are interested in the asymptotic behaviour of solutions in the direction of silent singularities. The main conclusion is that, for a…
In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional curvature we prove that the static and…
An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the `outside' is then…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable…
We present a method to generate static solutions in the Einstein-Maxwell system with a (phantom) dilaton field in $n(\ge 4)$-dimensions, based upon the symmetry of the target space for the nonlinear sigma model. Unlike the conventional…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
This is the second part of a series of papers proving the nonlinear stability of a one-parameter family of continuous self-similar $C^{1,\alpha}$ naked singularity solutions, with $0<\alpha\ll1$, to the spherically symmetric Einstein-scalar…
Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions.…
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
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…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all…
We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
We present the asymptotic solutions for spacetimes with non-zero cosmological constant $\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose)…
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…