Related papers: Gluing and wormholes for the Einstein constraint e…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…
We first show that the connected sum along submanifolds introduced by the second author for compact initial data sets of the vacuum Einstein system can be adapted to the asymptotically Euclidean and to the asymptotically hyperbolic context.…
We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.
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 give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
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 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…
Wormhole solutions in gravitational theories typically require exotic matter. Here we present a wormhole solution to the field equations of Einsteinian Cubic Gravity -- a phenomenological competitor to general relativity that includes terms…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
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…
Spacetime wormholes are evidently an essential component of the construction of a time machine. Within the context of general relativity, such objects require, for their formation, exotic matter -- matter that violates at least one of the…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to…
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…
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
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…
We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in $H^s$ where $s>3/2$. The constant mean curvature (CMC) conformal method leads to a…
We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…