Related papers: The Framework, Causal and Co-compact Structure of …

We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie…

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we…

We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing 4-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by…

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…

I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume…

Ori and Soen have proposed a spacetime which has closed causal curves on the boundary of a region of normal causality, all within a region where the weak energy condition (positive energy density) is satisfied. I analyze the causal…

We study notions of conjugate points along timelike geodesics in the synthetic setting of Lorentzian (pre-)length spaces, inspired by earlier work for metric spaces by Shankar--Sormani. After preliminary considerations on convergence of…

We offer a mathematically rigorous basis for the widely held suspicion that full black hole evaporation is in tension with predictability. Based on conditions expressing the global causal structure of evaporating black hole spacetimes, we…

We study the interplay between the global causal and geometric structures of a spacetime $(M,g)$ and the features of a given smooth $\mathbb{R}$-action $\rho$ on $M$ whose orbits are all causal curves, building on classic results about Lie…

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying…

We generalize simplicial minisuperspace models associated with restricting the topology of the universe to be that of a cone over a closed connected combinatorial $3-$manifold by considering the presence of a massive scalar field. By…

The spacetime of Ho and Weiler [Phys. Rev. D {\bf 87}, 045004 (2013)] supposedly admitting closed timelike curves (CTCs) is flat Minkowski spacetime with a compactified coordinate and can only contain CTCs if the compact direction is chosen…

When studying the causal propagation of a field in a globally hyperbolic spacetime M, one often wants to express the physical intuition that it has compact support in spacelike directions, or that its support is a spacelike compact set. We…

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

In this work we study the structure of the future causal completion $\hat{M}$ of a globally hyperbolic GRW spacetime $\mathbb{R}\times_\alpha M$ using the novel notion of Lorentzian pre-length spaces. As our main result, we prove that the…

It is shown that the warped product spacetime P=M *_f H, where H is a complete Riemannian manifold, and the original spacetime M share necessarily the same causality properties, the only exceptions being the properties of causal continuity…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

In this conference published in 1997 some problems on the geodesics of a Lorentzian manifold concerning causality and infinite-dimensional variational methods, are pointed out. Even though a big progress on many of these questions have been…

In this article we first observe that the Path topology of Hawking, King and MacCarthy is an analogue, in curved spacetimes, of a topology that was suggested by Zeeman as an alternative topology to his so-called Fine topology in Minkowski…