Related papers: The characteristic gluing problem for the Einstein…
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…
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
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 prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
It is possible to solve the Einstein constraint equations as an evolutionary rather than an elliptic system. Here we consider the Gauss constraint in electrodynamics as a toy model for thist. We use a combination of the evolutionary method…
In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of…
We consider the Einstein-dust equations with positive cosmological constant $\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the…
We review notions of mass of asymptotically locally Anti-de Sitter three-dimensional spacetimes, and apply them to some known solutions. For two-dimensional general relativistic initial data sets the mass is not invariant under asymptotic…
We give a new construction of conserved charges in asymptotically anti-de Sitter spacetimes in Einstein's gravity. The new formula is explicitly gauge-invariant and makes direct use of the linearized curvature tensor instead of the metric…
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein…
This article is the second of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. In the present article, we record geometric conclusions obtained by combining the geometric framework…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
We consider the formation of trapped surfaces in the evolution of the Einstein-scalar field system without symmetries. To this end, we follow An's strategy to analyse the formation of trapped surfaces in vacuum and for the Einstein-Maxwell…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…