Related papers: The problem of characterising stationary data for …
Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
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 study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$…
We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-aether theory. The latter is a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical timelike 'aether' vector field,…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…
We show how to solve the Cauchy problem for the Einstein-Vlasov equations with geometric initial data on a light-cone.
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source,…
New similarity variables are introduced for the Einstein - Maxwell equations with one Killing vector that reduce the non-linear partial differential equations in three independent variables to ordinary differential equations. These…
This is the second part of our result on a class of global characteristic problems for the Einstein vacuum equations with small initial data. In the previous work denoted by (I), our attention was focused on prescribing the initial data…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…
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…