Related papers: On Coordinate Frames in Axisymmetric Static Vacuum…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
We discuss how inhomogeneities of the universe affect observations of the gravitational lensing; (1) the bending angle, (2) the lensing statistics and (3) the time delay. In order to take account of the inhomogeneities, the Dyer-Roeder…
A spherically symmetric and static metric that describes physical coordinates is introduced. It is defined to be a metric that gives coordinate independent results for physically observable quantities without a further coordinate…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
Symmetry contributes to processes of perceptual organization in biological vision and influences the quality and time of goal directed decision making in animals and humans, as discussed in recent work on the examples of symmetry of things…
It has been proposed that the observed dark energy can be explained away by the effect of large-scale nonlinear inhomogeneities. In the present paper we discuss how observations constrain cosmological models featuring large voids. We start…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of…
Despite the assumption that an ideal FLRW observer is not dependent on the local environment, observations are biased by the positions of the observers due to the matter correlations in the large-scale structure (LSS) of the universe. The…
We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore,…
This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to characterize…
In real-world scene perception human observers generate sequences of fixations to move image patches into the high-acuity center of the visual field. Models of visual attention developed over the last 25 years aim to predict two-dimensional…
We study the spatial dependence of the quantum friction effect for an atom moving at a constant velocity, in a parallel direction to a material plane. In particular, we determine the probability per unit time and unit area, for exciting…
This work addresses the problem of designing an equivariant observer for a first order dynamical system on the unit-sphere. Building upon the established case of unit bearing vector dynamics with angular velocity inputs, we introduce an…
We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of…
The homogeneous and isotropic radiation dominated universe, following the inflationary stage, is expressed as a spherically symmetric and inhomogeneous spacetime upon a power law type conformal transformation of the null (cosmological)…
For observers in curved spacetimes, elements of the dual space of the set of linearized Poincar\'e transformations from an observer's tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an…
Energy-dependent speeds of light have been considered an observable signature of quantum gravity effects. The two simplest dispersion relationships produce either linear or quadratic corrections, in particle energy, to the photon speed. The…
Location dependence of physical parameters such as the electromagnetic fine structure constant and Newton's G produce body accelerations which violate universality of free fall rates testable with laboratory and space experiments.…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is…