Related papers: Compact hyperbolic universe and singularities

The spacetime structure of the spatially uniformly expanding universe is described in terms of a kind of global space and global time instead of the space and time we usually recognize. The global space at some instant is a space in which…

Smooth spacetimes with a compact Cauchy horizon ruled by closed null geodesics are considered. The compact Cauchy horizon is assumed to be non-degenerate. Then, supporting the validity of Penrose's strong cosmic censor hypothesis, the…

The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched.…

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\phi )=A\phi ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first…

Observations of the cosmic microwave sky are revealing the primordial non-uniformities from which all structure in the Universe grew. The only known physical mechanism for generating the inhomogeneities we see involves the amplification of…

The general world model for homogeneous and isotropic universe has been roposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a 5-dimensional space-time that is embedding…

Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite…

We investigate cosmic censorship in anti-de Sitter space in holographic models in which the ground state is described by a good singularity. These include supersymmetric truncations of string/M-theory, for which a positive-energy theorem…

The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall…

Theoretical considerations motivate us to consider vacuum energy to be able to decay and to assume that the spatial geometry of the universe is closed. Combining both aspects leads to the possibility that the universe, or certain regions…

Improving a singularity theorem in General Relativity by Galloway and Ling we show the following (cf.\ Theorem 1): If a globally hyperbolic spacetime $M$ satisfying the null energy condition contains a closed, spacelike Cauchy surface…

The paper initiates a systematic study of Moebius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is Moebius equivalent to the boundary at infinity of a rank one symmetric…

A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…

Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is…

Performing a fully non-perturbative analysis using the tools of numerical general relativity, we demonstrate that a period of slow contraction is a `supersmoothing' cosmological phase that homogenizes, isotropizes and flattens the universe…

The present-day Universe appears to be homogeneous on very large scales. Yet when the casual structure of the early Universe is considered, it becomes apparent that the early Universe must have been highly inhomogeneous. The current…

We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points…

In recent years, the large angle COBE--DMR data have been used to place constraints on the size and shape of certain topologically compact models of the universe. Here we show that this approach does not work for generic compact models. In…

One can make the very simple hypothesis that the Universe is the inside of an hypersphere in 4 dimensions, where our 3-dimensional world consists of hypersurfaces at different radii. Based on this assumption it is possible to show that…

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…