Related papers: On the causal hierarchy of Lorentzian length space…

Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related…

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 full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…

Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.

It is well-known that global hyperbolicity implies that the Lorentzian distance is finite and continuous. By carefully analysing the causes of discontinuity of the Lorentzian distance, we show that in most other respects the finiteness and…

In this work we revisit the notion of the (future) causal completion of a globally hyperbolic spacetime and endow it with the structure of a Lorentzian pre-length space. We further carry out this construction for a certain class of…

The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on…

We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the…

A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. In this note we give…

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…

We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are…

We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global…

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The…

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…

We investigate the compatibility of Lorentzian amalgamation with various properties of Lorentzian pre-length spaces. In particular, we give conditions under which gluing of Lorentzian length spaces yields again a Lorentzian length space and…

After the heroic epoch of Causality Theory, problems concerning the smoothability of time functions and Cauchy hypersurfaces remained as unanswered folk questions. Just recently solved, our aim is to discuss the state of the art on this…

This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly causal Lorentzian manifolds to the corresponding category of…

We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary ``positive signature'' metrics or other unobserved fields. We begin…

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal…

We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when…