Related papers: Basel problem: a physicist's solution
We consider a Hubble expansion law modified in the infra-red by distance-dependent terms, and attempt to enforce homogeneity upon it. As a warm-up, we re-derive the basic kinematics of a Friedman Robertson Walker universe without using…
Baryon asymmetry of the observed universe as a clue to a resolution of dark matter, galaxy formation and other standard model problems.
We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the…
A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass…
The standard method of modelling axisymmetric stellar systems begins from the assumption that mass follows light. The gravitational potential is then derived from the luminosity distribution, and a unique two-integral distribution function…
In this paper, we present a "stellar dynamics" model of an infinite Universe, where matter distribution follows an inverse proportionality squared relationship with respect to the distance from the rotation center of galaxy clusters and…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
We consider the Einstein-Maxwell system of equations in the context of isotropic coordinates for matter distributions with anisotropy in the presence of an electric field. We assume a polytropic equation of state for the matter…
Some of the assumptions of cosmology, as based on the simplest version of General Relativity, are discussed. It is argued that by slight modifications of standard gravitation theory, our notion of the sources of gravity {the right hand side…
A dual optical set-up is proposed to detect simultaneously the different behavior of light from stellar and local sources, in relation to speed-induced aberration. A small laser is set at the center of the objective lens of a telescope,…
We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of…
We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction. It is natural to apply Born-Oppenheimer approximation to this problem. We present a detailed…
We propose a new mechanism to solve the fine-tuning problem. We start from a multi-local action $ S=\sum_{i}c_{i}S_{i}+\sum_{i,j}c_{i,j}S_{i}S_{j}+\sum_{i,j,k}c_{i,j,k}S_{i}S_{j}S_{k}+\cdots$, where $S_{i}$'s are ordinary local actions.…
The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
In this short note, we present a probabilistic perspective on the Schiffer's problem in the inverse scattering theory, which asks whether one can uniquely determine the shape of an unknown obstacle by a single far-field measurement. It is a…
The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We consider light propagation in an inhomogeneous irrotational dust universe with vanishing cosmological constant, with initial conditions as in standard linear perturbation theory. A non-perturbative approach to the dynamics of such a…