Related papers: Flat, Uniformly Expanding Space in five Exercises
We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…
We study a new construction of bodies from a given convex body in $\mathbb{R}^{n}$ which are isomorphic to (weighted) floating bodies. We establish several properties of this new construction, including its relation to $p$-affine surface…
We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two…
The meaning of the expansion of the universe, or the `expansion of space,' is explored using two phenomena: the motion of a test particle against a homogeneous background and the cosmological redshift. Contrary to some expectations, a…
We study the problem of the motion of the free surface of a liquid. We prove existence and stability for the linearized equations.
Increasing astronomical evidence indicates that the expansion of the universe is accelerating. By simply solving Einstein equations we show in this letter that a wide class of generic quintessence models leading to eternal acceleration is…
A modern elementary introduction to special relativity for advanced school children or first-year university students, in Russian. I try to demonstrate that relativity does not contradict common sense; on the contrary, it follows from…
The specialised uses of solid angles mean that they are quite unfamiliar quantities. This article, apart from making solid angles a little more familiar, brings out several topics of general interest, such as how units are interrelated and…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both equations. We construct explicit solutions showing the…
Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the…
A modification to the Friedmann Robertson Walker equation is proposed in which the universe is flat, matter dominated, and accelerating. An additional term, which contains only matter or radiation (no vacuum contribution), becomes the…
We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with…
We consider an Einstein-Maxwell action modified by the addition of three terms coupling the electromagnetic strength to the curvature tensor. The corresponding generalized Maxwell equations imply a variation of the speed of light in a…
This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete…
This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration,…
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of…
These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…
In this note, we discuss how possible expansion histories of the universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing…
The speed of light is usually taken as one of the fundamental constants. String, and field, theories appear to require the altercation of this constant into a functional form $E(m,c)$ which is not $E=mc^2$. The analysis requires the…