Related papers: Selfgravitating nonlinear scalar fields
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…
In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…
We consider the strategy of realizing the solution of a Cauchy problem with radial data as a limit of radial solutions to initial-boundary value problems posed on the exterior of vanishing balls centered at the origin. The goal is to gauge…
We show that the spherically symmetric Einstein-scalar-field equations for small slowly particle-like decaying initial data at null infinity have unique global solutions.
We prove the global existence and uniqueness of classical solutions with small initial data and with wake-like decaying null infinity for the spherically symmetric Einstein-scalar-field equations with potential, where the scalar potential V…
The subject of this article is the structure of big bang singularities in spatially homogeneous solutions to the Einstein non-linear scalar field equations. In particular, we focus on Bianchi class A; i.e., developments arising from left…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field…
We establish the global existence and precise estimates of a class of singularity-free cosmological solutions in nonlinear Einstein-scalar-Gauss-Bonnet (ESGB) gravity with quadratic coupling, in close agreement with previous numerical…
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…
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as…
We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…
The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the…
We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial…
In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density…
We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological…
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform…
We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the…