相关论文: The conformal Einstein field equations and the loc…

We study the relationship between asymptotic characteristic initial data at past null infinity and the regularity of solutions at future null infinity for the massless linear spin-s field equations on Minkowski space. By quantitatively…

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…

We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity,…

This is the second part of our result on a class of global characteristic problems for the Einstein vacuum equations with small initial data. In the previous work denoted by (I), our attention was focused on prescribing the initial data…

We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…

Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving…

The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…

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…

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…

In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…

In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…

We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut…

In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…

We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…

Several calculations in conformally static spacetimes rely on the introduction of an ultrastatic background. I describe the general properties of ultrastatic spacetimes, and then focus on the problem of whether a given spacetime can be…

We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…

We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…

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…