Related papers: Vacuum initial data with minimal decay and borderl…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
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 study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
This paper proves the stability, with respect to the evolution determined by the vacuum Einstein equations, of the Cartesian product of high-dimensional Minkowski space with a compact, Ricci-flat Riemannian manifold that admits a spin…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to time $e^{C/\epsilon^2}$ while $e^{C/\epsilon^2}$ is also the…
We present novel classes of non-stationary solutions to the five-dimensional generalized Einstein-Maxwell-dilaton theory with cosmological constant, in which the Maxwell's filed and the cosmological constant couple to the dilaton field. In…
We prove that the charge-scalar field (also known as the massless Maxwell-Klein-Gordon) equations are globally stable on (3+1) dimensional Minkowski space for small initial data in certain gauge covariant weighted Sobolev spaces. These…
We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bartnik data condition involving spacetime rotations, and…
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In…
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity…
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…
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the…
In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out…
A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first…
We construct local solutions to the Benjamin-Ono equation for quasi-periodic initial data. The solution is unique among limits of smooth solutions and depends continuously on the data. Our result applies to a richer class of quasi-periodic…
The initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a challenging open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without…
This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered…
We prove a global in time existence theorem for the initial values problem for the Einstein-Boltzmann system with cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.