Related papers: Gluing construction of initial data with Kerr-de S…
Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…
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,…
We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a…
We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic surfaces in static vacuum four-dimensional backgrounds with cosmological constant $\Lambda \in \mathbb{R}$ and arbitrary…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
We study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi)…
Using a metric conformal formulation of the Einstein equations, we develop a construction of 4-dimensional anti-de Sitter-like spacetimes coupled to tracefree matter models. Our strategy relies on the formulation of an initial-boundary…
In the present paper a global conformal invariant $Y$ of a closed initial data set is constructed. A spacelike hypersurface $\Sigma$ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation ${\cal D}_e$, the…
We review the Carlotto-Schoen construction of general relativistic initial data sets which are trivial outside of cones, discuss the context, the implications, and some further developments.
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime…
This short note is a follow-up on the paper by Beig and Chru\'sciel regarding the use of potentials to perform a gluing and shielding of initial data for Maxwell fields and linearised gravity. Based on a work in collaboration with Andersson…
Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing…
A class of vacuum initial-data sets is described which are based on certain expressions for the extrinsic curvature first studied and employed by Bowen and York. These expressions play a role for the momentum constraint of general…
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…
We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…
We construct exact initial data for closed cosmological models filled with regularly arranged black holes in the presence of $\Lambda$. The intrinsic geometry of the 3-dimensional space described by this data is a sum of simple closed-form…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of…