Related papers: Characteristic Gluing with $\Lambda$ 1. Linearised…
We prove a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic hypersurfaces in static vacuum $(n+1)$-dimensional backgrounds with cosmological constant $ \Lambda \in \mathbb{R}$, $n\ge 4$.…
We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum $n$-dimensional backgrounds, $n\ge 3$, with any finite $k$, with…
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the…
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 analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When $\Lambda>0$ the energy…
We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised…
We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her…
The cosmological constant $\Lambda$ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of $\Lambda$ or $\Lambda$ being zero would describe…
We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $\Lambda \in {\mathbb R}^*$, generalising the definition of Trautman and Bondi for $\Lambda=0$.…
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 linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
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 establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions $d\ge 4$, with emphasis on characteristic data. A useful tool is provided by the…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
We study the nonlinear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of cosmological black holes, we construct the solution of the…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from…
We address the problem of consistent Campiglia-Laddha superrotations in $d>4$ by solving Bondi-Sachs gauge vacuum Einstein equations at the non-linear level with the most general boundary conditions preserving the null nature of infinity.…
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…
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…