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We begin with a basic exploration of the (point-set topological) notion of Hausdorff closed limits in the spacetime setting. Specifically, we show that this notion of limit is well suited to sequences of achronal sets, and use this to…
Although it is long believed that vanishing of chiral central charges of a 2d conformal field theory (CFT) implies the existence of conformal boundary conditions, there are yet higher obstructions. In this paper, we focus on 2d rational…
A new speculative model for the expansion of our universe has been under development by the author for the last two decades, which correctly predicts astronomical measurements with no dark matter or dark energy. This new closed model (no…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
We summarise the new conformal framework of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity. Both new definitions are motivated by, but not restricted to quiescent cosmology and the Weyl curvature hypothesis,…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…
A new approach for treating boundary Poisson structures based on causality and locality analysis is proposed for a single scalar field with boundary interaction. For the case of linear boundary condition, it is shown that the usual…
Limit and Pseudotopological spaces are two generalizations of topological spaces which are defined by indicating what filters converge under some axioms. In this article, we introduce covering spaces and set forth some necessary conditions…
Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory,…
We discuss solutions of several questions concerning the geometry of conformal planes.
We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in a finite time evolution. We show that such a boundary is not a failure of the moduli space approach but has a…
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…
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Cosmological models may result in future singularities. We show that, in the framework of dynamical varying speed of light theories, it is possible to regularize those singularities.
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these…
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…