Related papers: The annoying null boundaries
The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive…
We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
We study the evolution of bubble spacetimes in vacuum and electrovac scenarios by numerical means. We find strong evidence against the formation of naked singularities in (i) scenarios with negative masses displaying initially collapsing…
We prove that the space of causal curves between compact subsets of a separable globally hyperbolic poset is itself compact in the Vietoris topology. Although this result implies the usual result in general relativity, its proof does not…
We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard…
We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $H^k(S)$ ($k > 2$). Through an elaborate geometric construction, we show that for any $T >0$, the time $T$…
Assume that $(X, g^+)$ is an asymptotically hyperbolic manifold, $(M, [\bar{h}])$ is its conformal infinity, $\rho$ is the geodesic boundary defining function associated to $\bar{h}$ and $\bar{g} = \rho^2 g^+$. For any $\gamma \in (0,1)$,…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…
We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension…
Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…
In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length…
We study the geometry of null hypersurfaces in indefinite complex contact manifolds. We prove several classification results for a variety of well-known null hypersurfaces, including the totally umbilic, totally screen umbilic, and the…
In this talk a previous theorem on geodesic completeness of diagonal cylindrical spacetimes will be generalized to cope with the nondiagonal case. A sufficient condition for such spacetimes to be causally geodesically complete will be given
The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the…
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…
In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…
We show that timelike maximal cylinders in $\RR^{1 + 2}$ always develop singularities in finite time and that, infinitesimally at a generic singularity, their time slices are evolved by a rigid motion or a self-similar motion. We also prove…
Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in…
Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…