Related papers: Gluing construction of initial data with Kerr-de S…
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter…
We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the flat case with prescribed support properties. These results…
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are…
In this paper we develop a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to the…
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be…
We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
We construct numerically time-symmetric initial data that are Schwarzschildean at spatial infinity and Brill-Lindquist in the interior. The transition between these two data sets takes place along a finite gluing region equipped with an…
We describe a numerical method to construct Cauchy data extending to space-like infinity based on Corvino's (2000) gluing method. Adopting the setting of Giulini and Holzegel (2005), we restrict ourselves here to vacuum axisymmetric…
We prove a strong localized gluing result for the general relativistic constraint equations (with or without cosmological constant) in $n\geq 3$ spatial dimensions. We glue an $\epsilon$-rescaling of an asymptotically flat data set…
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the…
Generalising an analysis of Corvino and Schoen, we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces. As a corollary we prove several perturbation, gluing, and extension…
We present a procedure for asymptotic gluing of hyperboloidal initial data sets that preserves the shear-free condition. Our construction is modeled on a previous gluing construction by the last three named authors, but with significant…
We construct large classes of vacuum general relativistic initial data sets, possibly with a cosmological constant Lambda, containing ends of cylindrical type.
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
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…
This is the third paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We provide full details of our characteristic gluing (including the $10$ charges) of strongly asymptotically flat…
In this paper we introduce the characteristic gluing problem for the Einstein vacuum equations. We present a codimension-$10$ gluing construction for characteristic initial data which are close to the Minkowski data and we show that the…
We construct non-trivial vacuum space-times with a global Scri. The construction proceeds by proving extension results across compact boundaries for initial data sets, adapting the gluing arguments of Corvino and Schoen. Another application…
Building on the work of Giulini and Holzegel (2005), a new numerical approach is developed for computing Cauchy data for Einstein's equations by gluing a Schwarzschild end to a Brill-Lindquist metric via a Corvino-type construction. In…