Related papers: Recollapse of the closed Tolman spacetimes
The closed-universe recollapse conjecture is studied for a class of closed spherically symmetric spacetimes which includes those having as a matter source: (1) a massless scalar field; (2) a perfect fluid obeying the equation of state $\rho…
It is proven that any spherically symmetric spacetime that possesses a compact Cauchy surface $\Sigma$ and that satisfies the dominant-energy and non-negative-pressures conditions must have a finite lifetime in the sense that all timelike…
We prove that the maximal development of any spherically symmetric spacetime with collisionless matter (obeying the Vlasov equation) or a massless scalar field (obeying the massless wave equation) and possessing a constant mean curvature…
Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction…
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…
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…
Gravitational collapse of radiation shells in a non self-similar higher dimensional spherically symmetric spacetime is studied. Strong curvature naked singularities form for a highly inhomogeneous collapse, violating the cosmic censorship…
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…
We establish a new CMC (constant mean curvature) existence result for cosmological spacetimes, i.e., globally hyperbolic spacetimes with compact Cauchy surfaces satisfying the strong energy condition. If the spacetime contains an expanding…
All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the…
A physically plausible Lema{\^{\i}}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that…
We explore numerically the evolution of a collapsing spherical shell of charged, massless scalar field. We obtain an external \RN space-time, and an inner space-time that is bounded by a singularity on the Cauchy Horizon. We compare these…
Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic…
We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\pi$. Here strong spacelike means that the tangent…
We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The…
In this note, we prove analytic bounds on the equation of state of a cosmological fluid composed of an arbitrary number of canonical scalars evolving in a negative multi-exponential potential. Because of the negative energy, the universe is…
Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices.…
We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the $R+\alpha R^{2}$ theory. By including ordinary matter, we…
This article gives necessary and sufficient conditions for the formation of trapped surfaces in spherically symmetric initial data defined on a closed manifold. Such trapped surfaces surround a region in which there occurs an enhancement of…
We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable…