Related papers: The causal hierarchy of spacetimes
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…
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…
Cosmology today is confronted with several seemingly insoluble puzzles and strange, inexplicable coincidences. But a careful re-examination of the Cosmological principle and the Weyl postulate, foundational elements in this subject,…
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
In this report we discuss the organization of different levels of nature and the corresponding space-time structures by the consideration of a particular problem of time irreversibility. The fundamental time irreversibility problem consists…
We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
We investigate three causality-violating spacetimes: Misner space (including Kip Thorne's "moving wall" model), the pseudo-Schwarzschild spacetime, and a new model introduced here, the pseudo-Reissner-Nordstr\"{o}m spacetime. Despite their…
We give a brief review of recent developments in five-dimensional theories of spacetime and highlight their geometrical structure mainly in connection with the Campbell-Magaard theorem.
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
The concept of the space-time as emerging in the world phase transition, vs. a priori exiting, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications for…
It is shown that if $M$ is a strongly causal free of naked singularities space-time, then its causal structure is completely characterized by a partial order in the space of skies defined by means of a class non-negative Legendrian…
The discovery of universe's late-time acceleration and dark energy has overseen a great deal of research into cosmological singularities and in this brief review, we discuss all the prominent developments in this field for the best part of…
We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be…
Physical foundations for relativistic spacetimes are revisited, in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of Special Relativity and Classical…
Complex systems can be described at myriad different scales, and their causal workings often have multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and…
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…
The mechanism of continuous set of different universes formation is elaborated. It provides tool to solve the problem of observed smallness of physical parameters. Solution of two puzzles - the hierarchy and the cosmological constant…
The machinery is suggested to describe the varying spacetime topology on the level of its substitutes by finite topological spaces.