Related papers: Class A Spacetimes
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
We introduce the notion of causally-null-compactifiable space-times which can be canonically converted into a compact timed-metric-spaces using the cosmological time of Andersson-Howard-Galloway and the null distance of Sormani-Vega. We…
We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of…
A class of Riemann-Cartan G\"odel-type space-times are examined in the light of the equivalence problem techniques. The conditions for local space-time homogeneity are derived, generalizing previous works on Riemannian G\"odel-type…
We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…
Being motivated by the notions of $\kappa$-Fr\'{e}chet--Urysohn spaces and $k'$-spaces introduced by Arhangel'skii, the notion of sequential spaces and the study of Ascoli spaces, we introduce three new classes of compact-type spaces. They…
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…
Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\ the set of causally related pairs…
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…
Margulis spacetimes are complete affine 3-manifolds that were introduced to show that the cocompactness condition of Auslander's conjecture is necessary. There are Lorentzian manifolds that are obtained as a quotient of the three…
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…
Let $\mathbf{E}$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete flat Lorentzian $3$-manifold $\mathbf{E}/\Gamma$ with a free holonomy group $\Gamma$ of rank $\mathbf{g}, \mathbf{g} \geq 2$.…
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…
In this article spacelike hypersurfaces immersed in twisted product spacetimes $I\times_f F$ with complete fiber are studied. Several conditions ensuring global hyperbolicity are presented, as well as a relation that needs to hold on each…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…
The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…
For any finite abelian group G, we study the moduli space of abelian $G$-covers of elliptic curves, in particular identifying the irreducible components of the moduli space. We prove that, in the totally ramified case, the moduli space has…
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…
Let ${\mathcal M}_{g,n}$ denote the moduli space of smooth, genus $g\geq 1$ curves with $n\geq 0$ marked points. Let ${\mathcal A}_h$ denote the moduli space of $h$-dimensional, principally polarized abelian varieties. Let $g\geq 3$ and…