Related papers: Global hyperbolicity and factorization in cosmolog…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
The presence of additional compact dimensions in cosmological models is studied in the context of modified teleparallel theories of gravity. We focus the analysis on eleven dimensional spacetimes, where the seven dimensional extra…
In this work we study an alternative topological model for explaining the observed acceleration of space-time, we answer the question of whether this acceleration could be a consequence of the topology of the universe. For doing that, we…
We discuss how the vector nature of magnetic fields, and the geometrical interpretation of gravity introduced by general relativity, lead to a special coupling between magnetism and spacetime curvature. This magneto-geometrical interaction…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
A new vector-tensor model of classical gravity, which contains coupling between the field strength of the vector field and the curvature tensors in six dimensions, is proposed. Cosmological solutions of the scale factors in this model with…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
We consider an extension of Weyl geometry with the most general connection linearly determined by a vector field. We discuss some of the geometrical properties within this framework and then we construct gravitational theories leading to an…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of…
In this review we discuss the global geometry of noncommutative field theories from a deformation point of view: The space-times under consideration are deformations of classical space-time manifolds using star products. Then matter fields…
A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a…