Related papers: Initial data sets with ends of cylindrical type: I…
We construct solutions of the vacuum vector constraint equations on manifolds with cylindrical ends.
A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no…
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 revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which…
On any closed Riemannian manifold of dimension greater than $7$, we construct examples of background physical coefficients for which the Einstein-Lichnerowicz equation possesses a non-compact set of positive solutions. This yields in…
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
A vacuum type D initial data set is a vacuum initial data set of the Einstein field equations whose data development contains a region where the space-time is of Petrov type D. In this paper we give a {\em systematic} characterisation of a…
In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in…
We construct manifold structures on various sets of solutions of the general relativistic initial data sets.
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane…
This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York,…
A generalization of the Bowen-York initial data to the case with a positive cosmological constant is investigated. We follow the construction presented recently by Bizo\'n, Pletka and Simon, and solve numerically the Lichnerowicz equation…
We apply the conformal method to solve the initial value formulation of general relativity to the $\lambda$-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. We…
Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the…
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
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…
We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the…
We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's…