Related papers: Topological Censorship
CMC (constant mean curvature) Cauchy surfaces play an important role in mathematical relativity as finding solutions to the vacuum Einstein constraint equations is made much simpler by assuming CMC initial data. However, in [2] Bartnik…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983…
We survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes containing a compact Cauchy surface. We consider spacetimes with an $\ell$-dimensional Lie algebra of space-like Killing fields.…
This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are…
We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the…
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes…
Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such…
Transforming Penrose's intuitive picture of a strong cosmic censorship principle, that generically forbids the appearance of locally naked space-time singularities, into a formal mathematical proof, remains at present, one of the most…
This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the…
In this paper we study the flat (n+1)-spacetimes admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold. We show how to construct a canonical future complete one among all such spacetimes sharing the same holonomy. We…
In this article, we extend a construction of [6] to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form $M \# M$, where $M$ is…
New general results of non-existence and rigidity of spacelike submanifolds immersed in a spacetime, whose mean curvature is a time-oriented causal vector field, are given. These results hold for a wide class of spacetimes which includes…
Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe…
Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foliations of this kind in…
In general relativity, nonsingular black holes contain (at least) a Cauchy horizon, a null hypersurface beyond which determinism breaks down. Even though the strong cosmic censorship conjecture establishes the impossibility of extending…
We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence…
The cosmic censorship conjecture posits that singularities forming to the future of a regular Cauchy surface are hidden by an event horizon. Consequently any topological structures will ultimately collapse within the horizon of a set of…
Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti-de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful…