Related papers: A note on spacelike and timelike compactness

Let ${\cal H}$ be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that ${\cal H}$ has compact closure in moduli space if and only if neither attractor is a fixed point.

Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological…

We consider the behaviour of the cosmological acceleration for time-dependent hyperbolic and flux compactifications of M-theory, with an exponential potential. For flat and closed cosmologies it is seen that a positive acceleration is…

The building of a time machine, if possible at all, requires the relevant regions of spacetime to be compact (that is, physically speaking, free from sources of unpredictability such as infinities and singularities). Motivated by this…

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.

The zoology of singularities for Lorentzian manifold is slightly more complicated than for Riemannian manifolds. Our present work study Cauchy-compact globally hyperbolic singular flat spacetimes with extreme BTZ-like singular lines. We use…

The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous…

Since the solution of the so-called folk problems of smoothability, there has been a special interest in the properties of classical time and volume functions of spacetimes. Here we supply some information that complements the one provided…

This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced…

In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…

According to the work of Dennis Sullivan, there exists a smooth flow on the 5-sphere all of whose orbits are periodic although there is no uniform bound on their periods. The question addressed in this article is whether these type of…

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…

Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\"u}ller space. We notice that…

We prove that global hyperbolicity is stable in the interval topology on the spacetime metrics. We also prove that every globally hyperbolic spacetime admits a Cauchy hypersurface which remains Cauchy under small perturbations of the…

We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…

The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…

In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions. Under antisymmetry this property, also known as…

Uniformly star superparacompactness, which is a topological property between compactness and completeness, can be characterized using finite-component covers and a measure of strong local compactness. Using these finite-component covers and…

In this paper, we investigate the initial value problem for symmetric hyperbolic systems on globally hyperbolic Lorentzian manifolds with potentials that are both nonlocal in time and space. When the potential is retarded and uniformly…

In this paper we consider the compactness of $\beta$-symplectic critical surfaces in a K\"ahler surface. Let $M$ be a compact K\"ahler surface and $\Sigma_i\subset M$ be a sequence of closed $\beta_i$-symplectic critical surfaces with…