Related papers: The Framework, Causal and Co-compact Structure of …
We consider 4-dimensional spacetime manifolds that are piecewise Lorentzian, where the Lorentzian components of the manifold are separated by codimension-one planes (spacelike or timelike) on which the metric is degenerate. Such manifolds…
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 study open orbits of symmetric subgroups of a simple connected Lie group G on a causal flag manifold. First we show that a flag manifold M of G carries an invariant causal structure if and only if G is hermitian of tube type and M is the…
Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime--from a General-Relativistic point of view. But this does not mean that it is…
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian…
Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time…
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on…
We show that the Goedel solution of five-dimensional gauged supergravity contains either closed time-like curves through every space-time point or none at all, dependent on the rotational parameter. In addition, we present a deformation of…
A hairy extension of the Bertotti-Robinson regular spacetime has been recently introduced in the context of the Einstein-Maxwell-Scaler theory that surprisingly is a singular black hole formed in the $S_{3}$ background spatial topology…
We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy…
The hyperbolic components in the moduli space ${M}_d$ of degree $d\geq2$ rational maps are mysterious and fundamental topological objects. For those in the connectedness locus, they are known to be the finite quotients of the Euclidean…
A new general procedure to construct realistic spacetimes is introduced. It is based on the null congruence on a time-oriented Lorentzian manifold associated to a certain timelike vector field. As an application, new examples of stably…
In order to include nontrivial spatial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.
We derive the dynamics of (isotropic) scalar perturbations from the mean-field hydrodynamics of full Lorentzian quantum gravity, as described by a two-sector (timelike and spacelike) Barrett-Crane group field theory (GFT) model. The rich…
We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every chain complete, rooted tree into a Fr\'echet--Urysohn,…
We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurston's Geometrization Conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations.…