Related papers: Free evolution of the hyperboloidal initial value …
The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose…
Bondi's approach to the construction of a coordinate system is used with a different choice of gauge, in accordance with which the radial coordinate r is an affine parameter, to cast the metric tensor into a form suitable for use with the…
When using the black hole exclusion (horizon boundary condition) technique, $K$ is usually nonzero and spatially variable, so none of the special cases of York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear York…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…
The definition of well-behaved coordinate charts for black hole spacetimes can be tricky, as they can lead for example to either unphysical coordinate singularities in the metric (e.g. $r=2M$ in the Schwarzschild black hole) or to an…
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null…
We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions…