相关论文: Unique continuation from infinity in asymptoticall…

We generalize our unique continuation results recently established for a class of linear and nonlinear wave equations $\Box_g \phi + \sigma \phi = \mathcal{G} ( \phi, \partial \phi )$ on asymptotically anti-de Sitter (aAdS) spacetimes to…

We reconsider the unique continuation property for a general class of tensorial Klein-Gordon equations of the form \begin{align*} \Box_{g} \phi + \sigma \phi = \mathcal{G}(\phi,\nabla \phi) \text{,} \qquad \sigma \in \mathbb{R} \end{align*}…

We consider the question of whether solutions of Klein--Gordon equations on asymptotically Anti-de Sitter spacetimes can be uniquely continued from the conformal boundary. Positive answers were first given by the second author with G.…

We revisit the propagation of classical scalar fields in a spacetime which is asymptotically anti-de Sitter. The lack of global hyperbolicity of the underlying background gives rise to an ambiguity in the dynamical evolution of solutions of…

Asymptotically anti-de Sitter space-times are considered in a general dimension $d\ge 4$. As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is the anti-de Sitter group (although there is an…

In this paper we describe the behavior of solutions of the Klein-Gordon equation, (Box_g+lambda)u=f, on Lorentzian manifolds (X^o,g) which are anti-de Sitter-like (AdS-like) at infinity. Such manifolds are Lorentzian analogues of the…

It is shown that an $(n+1)$-dimensional asymptotically anti-de Sitter solution of the Einstein-vacuum equations is locally isometric to pure anti-de Sitter spacetime near the conformal boundary if and only if the boundary metric is…

We initiate the study of the spherically symmetric Einstein-Klein-Gordon system in the presence of a negative cosmological constant, a model appearing frequently in the context of high-energy physics. Due to the lack of global hyperbolicity…

The null splitting theorem (proved in math.DG/9909158) is discussed. As an application, a uniqueness theorem for Minkowski space and for de Sitter space associated with the occurrence of null lines (inextendible globally achronal null…

We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In…

We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary…

A new proof of Friedrich's theorem on the existence and stability of asymptotically de Sitter spaces in 3+1 dimensions is given, which extends to all even dimensions. In addition, we characterize the possible limits of spaces which are…

We prove various uniqueness results from null infinity, for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the…

We investigate solutions that are dynamically evolving between asymptotically de Sitter and asymptotically anti-de Sitter regions in the context of Einstein gravity coupled to general matter fields in d dimensions. We demonstrate the…

We consider wave equations with a critically singular potential $\xi \cdot \sigma^{-2}$ diverging as an inverse square at a hypersurface $\sigma = 0$. Our aim is to construct counterexamples to unique continuation from $\sigma = 0$ for this…

We use the formulation of asymptotically anti-de Sitter boundary conditions given by Ashtekar and Magnon to obtain a coordinate expression for the general asymptotically AdeS metric in a neighbourhood of infinity. From this, we are able to…

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of…

We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space…

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all…

This article solves the initial boundary value problem for the vacuum Einstein equations with a negative cosmological constant in dimension 4, giving rise to asymptotically Anti-de Sitter spaces. We introduce a new family of geometric…