Related papers: Geometric distances between closed universes
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
An approach to cosmological modelling is presented that incorporates the inhomogeneous structure of the Cosmic Web, specifically focusing on the interplay between cosmic voids and density walls. We extend the standard homogeneous and…
We consider the puzzle of cosmic voids bounded by two dimensional structures of galactic clusters as also a puzzle pointed out by Weinberg: How can the mass of a typical elementary particle depend on a cosmic parameter like the Hubble…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one…
The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the "beem's" construction. One can considere it as weak or so-called finite element method's approximation with…
Modern cosmology is closely linked to our understanding of radial null geodesics as these model the propagation of light signals through an expanding universe. Azimuthal geodesics, on the other hand, are perhaps best known for their…
Revolutionary advances in both theory and technology have launched cosmology into its most exciting period of discovery yet. Unanticipated components of the universe have been identified, promising ideas for understanding the basic features…
In some recent theories including Quantum SuperString theory we encounter duality - it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world…
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions of a rather smooth early universe to the present time? The answers to these questions will shed light on the cosmology we live…
Astronomers measure distances to faraway galaxies and their velocities. They do that in order to determine the expansion rate of the Universe. In Part I of these lectures the foundations of the theory of the expansion of the Universe was…
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their…
Almost all models of the universe start by assuming that matter fields can be modelled as dust. In the real universe, however, matter is clumped into dense objects that are separated by regions of space that are almost empty. If we are to…
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
We use the formalism of Geometrothermodynamics to derive a series of fundamental equations for thermodynamic systems. It is shown that all these fundamental equations can be used in the context of relativistic cosmology to derive diverse…