Related papers: The causal hierarchy of spacetimes
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…
There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is…
An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…
We investigate the causal structure of spacetimes $(M, g)$ for which the metric $g$ is singular on a set of points.
We begin with a brief summary of issues encountered involving causality in quantum theory, placing careful emphasis on the assumptions involved in results such as the EPR paradox and Bell's inequality. We critique some solutions to the…
We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
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…
Hawking's stable causality implies Sorkin and Woolgar's K-causality. The work investigates the possible equivalence between the two causality requirements, an issue which was first considered by H. Seifert and then raised again by R. Low…
An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of…
This short paper discusses continually updated causal abstractions as a potential direction of future research. The key idea is to revise the existing level of causal abstraction to a different level of detail that is both consistent with…
In a causal world the direction of the time arrow dictates how past causal events in a variable $X$ produce future effects in $Y$. $X$ is said to cause an effect in $Y$, if the predictability (uncertainty) about the future states of $Y$…
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…
By definition a spacetime is stably causal if it is possible to widen the light cones all over the spacetime without spoiling causality. We prove that if the spacetime is at least non-total imprisoning then it is stably causal provided the…
The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime are introduced and their relevance for the description of classical gravity discussed. A method to construct examples of such generalized…
Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian…
We overview our recent studies of cosmological models with expansion and global rotation. Problems of the early rotating models are discussed, and the class of new viable cosmologies is described in detail. Particular attention is paid to…
What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…
A new interpretation of the causality implementation in the Lienard-Wiechert solution raises new doubts against the validity of the Lorentz-Dirac equation and the limits of validity of the Minkowski structure of spacetime.
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…