Related papers: Causal Behaviour on Carter spacetime
Causal set quantum gravity is a Lorentzian approach to quantum gravity, based on the causal structure of spacetime. It models each spacetime configuration as a discrete causal network of spacetime points. As such, key questions of the…
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…
Reasonable spacetimes are non-compact and of dimension larger than two. We show that these spacetimes are globally hyperbolic if and only if the causal diamonds are compact. That is, there is no need to impose the causality condition, as it…
We prove that causal maximizers in $C^{0,1}$ spacetimes are either timelike or null. This question was posed in [17] since bubbling regions in $C^{0,\alpha}$ spacetimes ($\alpha <1$) can produce causal maximizers that contain a segment…
The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The…
Causal asymmetry is one of the great surprises in predictive modelling: the memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modelling a stochastic…
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, ${\sf x}$ can access ${\sf y}$ if an electromagnetic or (slower than light) mechanical signal could be sent from…
We describe a new class of models of quantum space-time based on energetic causal sets and show that under natural conditions space-time emerges from them. These are causal sets whose causal links are labelled by energy and momentum and…
Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local…
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we…
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…
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…
There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional…
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…
The Kasner spacetime is a cosmological model of an anisotropic expanding universe without matter and is an exact solution of the Einstein vacuum equations Ric(g) = 0. It is manifestly inextendible as a Lorentzian manifold with a twice…
Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Here…
The possibility of non-causal signal propagation is examined for various theories of dense matter. This investigation requires a discussion of definitions of causality, together with interpretations of spacetime position. Specific examples…
Higher-dimensional theories with time-like and space-like extra dimensions are compared both from the conceptual and from the phenomenological points of view. In this context causality and unitarity are discussed. It is shown that…
Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In…
According to Schopenhauer, Kant's arguments about the transcendental ideality of space and time can be extended to matter through the concept of causality and the principle of sufficient reason. In this article, I examine to what extent…