Related papers: A general theorem on temporal foliation of causal …
In this paper, we use our results concerning temporal foliations of causal sets in order to provide a new proof of Geroch's Theorem on temporal foliations in a globally hyperbolic spacetime.
A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can…
We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves…
We introduce a non-autonomous generalization of spatial-temporal differentiations, and prove results about probabilistically and topologically generic behaviors of certain spatial-temporal differentiations generated by endomorphisms of…
The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed.
We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…
Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related…
Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent…
The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
We present examples of foliations with infinite dimensional basic symplectic and com- plex cohomologies, along with a general sufficient condition for such phenomena. This puts re- strictions on possible generalizations of several…
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…
This work addresses the existence of transitive extensions of certain infinite permutation groups which arise as the automorphism groups of model-theoretic structures which are generic in the Fra\"iss\'e sense. The study of transitive…
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.
Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Algebraic and geometrical features of the set of timelets on a causal set are studied. A characterization of timelets in terms…
In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe…