Related papers: Theorems on Null-Paths and Red-Shift
A class of coordinate systems is found for Friedmann Cosmologies with local gravity such that it is possible to formulate quantum theory over astronomical and cosmological distances. When light from distance objects is treated as a quantum…
A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the…
Modern cosmological theory is based on the Friedmann--Robertson--Walker (FRW) metric. Often written in terms of co-moving coordinates, this well-known solution to Einstein's equations owes its elegant and highly practical formulation to the…
We provide a coordinate-free version of the local classification, due to A. G. Walker [Quart. J. Math. Oxford (2) 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as…
The aim of the present paper is to construct a field theory in the context of absolute parallelism (Teleparallel) geometry under the assumption that the canonical connection is semi-symmetric. The field equations are formulated using a…
We prove a generalisation of the Grothendieck-Riemann-Roch theorem, which is valid for any proper and flat morphism between noetherian and separated schemes of odd characteristic.
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…
Compatible equations, Singularities of solutions, Topological charges and quasi-charges. PhD thesis (translated frorm Russian). The book shows the sights of Absolute Parallelism (AP), and contains useful information on the problem of…
We explore in detail the 2+2 and 1+1+2 formalism in spherically symmetric spacetimes, spanning from deducing the dynamical equations to relating them to the well-known generalised Painlev\'e-Gullstrand (GPG) coordinate system. The evolution…
In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion.…
If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.
We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which…
We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological…
A direct and more general calculation of the limb effect connected with red-shift observations is obtained. Result agrees completely, in its general form, with that obtained from observations of the solar spectra but with different value…
The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold…
Contrary to general belief, the Fraunhofer lines have been found to be plasma redshifted and not gravitationally redshifted, when observed on Earth. Quantum mechanical effects cause the photons' gravitational redshift to be reversed as the…
Long before the general theory of relativity was finally formulated in 1916, arguments based entirely on Einstein's equivalence principle predicted the well known phenomenon of the gravitational red shift. Precisely the same arguments are…
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity.…