Related papers: K- causality and domain theory
As shown by Gott, a pair of straight cosmic strings moving in opposite directions, when they have suitable speed and impact parameter, produce closed timelike curves. I argue in this paper that there always is a not-so-frightening…
Causality is one of the fundamental structures of spacetimes, determining the possible behaviour and propagation of physical information. Causal structure can be analysed through the various modal logics it induces. The modal logics for the…
In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…
In this paper we establish that every (deterministic) non-autonomous, discrete-time, causal, time invariant system has a state-space representation, and discuss its minimality.
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
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…
We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…
The causal set approach to quantum gravity embodies the concepts of causality and discreteness. This article explores some foundational and conceptual issues within causal set theory.
We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the…
The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space,…
The additivity theorem for derivateurs associated to complicial biWaldhausen categories is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity,…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…
In this paper we attempt to explicate Salmon's idea of a causal process, as defined in terms of the mark method, in the context of C*-dynamical systems. We prove two propositions, one establishing mark manifestation infinitely many times…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where…
We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.