Related papers: Characteristic initial data and smoothness of Scri…
We derive necessary-and-sufficient conditions on characteristic initial data for Friedrich's conformal field equations in $3+1$ dimensions to have no logarithmic terms in an asymptotic expansion at null infinity.
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
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…
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…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
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…
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…
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…
We prove the existence of a large class of initial data for the vacuum Einstein equations which possess a finite number of asymptotically Euclidean and asymptotically conformally cylindrical or periodic ends. Aside from being asymptotically…
We describe our present understanding of the relations between the behaviour of asymptotically flat Cauchy data for Einstein's vacuum field equations near space-like infinity and the asymptotic behaviour of their evolution in time at null…
In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such…
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
We show how to solve the Cauchy problem for the Einstein-Vlasov equations with geometric initial data on a light-cone.
We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
We prove existence of solutions of the vacuum Einstein equations with initial data induced by a smooth metric on a light-cone.