Related papers: Causality and skies: is non-refocussing necessary?

Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of…

Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the…

Let $(M,g)$ be a spacetime. That is, $M$ is a real manifold of dimension $4$ equipped with a Lorentzian metric $g$. We show that any separation of time and space in $M$ is equivalent to introducing a (non-smooth) Riemann metric $h$. If $h$…

If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free…

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 discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric…

In this talk a previous theorem on geodesic completeness of diagonal cylindrical spacetimes will be generalized to cope with the nondiagonal case. A sufficient condition for such spacetimes to be causally geodesically complete will be given

We show a general theorem of existence of temporal foliations in a general causal set, under mild constraints. Then we study automorphisms of infinite causal sets (which satisfy further requirements) and show that they fall under one of two…

This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…

Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…

As well known, the b-boundaries of the closed Friedman world model and of Schwarzschild solution consist of a single point. We study this phenomenon in a broader context of differential and structured spaces. We show that it is an…

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime…

We explore the possibility that the entire departure of galactic rotational velocities from their luminous Newtonian expectation be cosmological in origin, and show that within the framework of conformal gravity (but not Einstein gravity…

We formulate the generalization of the Legendrian Low conjecture of Natario and Tod (proved by Nemirovski and myself before) to the case of causally simple spacetimes. We prove a weakened version of the corresponding statement. In all known…

We consider unitarity and causality in a higher-derivative theory of infinite order, where propagators fall off more quickly in the ultraviolet due to the presence of a transcendental entire function of the momentum. Like Lee-Wick theories,…

A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive…

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…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

Given a time function $\tau$ on a spacetime $M$, we define a `null distance function', $\hat{d}_\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla \tau$, we show that 1)…

The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…