相关论文: Angular distances in metric theories

The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay…

In relativistic physics, angular momentum is paired with a lesser known conserved quantity, the "mass moment", which appears as the time-space components of the angular momentum tensor. Calculations of mass moment in electromagnetic and…

We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…

Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded…

Modern astrometry is based on angular measurements at the micro-arcsecond level. At this accuracy a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem…

It is considered an equation for the Lyapunov exponent $% \gamma $ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of…

We investigate the optical properties of the solar gravitational lens (SGL) with respect to an extended source located at a large but finite distance from the Sun. The static, spherically symmetric gravitational field of the Sun is modeled…

Part A of this article is devoted to the general investigation of the gravitational-wave emission by post-Newtonian sources. We show how the radiation field far from the source, as well as its near-zone inner gravitational field, can (in…

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself.…

We use comparisons between the shapes of gravitational lens galaxies and models for their mass distributions to derive statistical constraints on the alignment of the mass distribution relative to the observed lens galaxy and on the…

In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean…

We prove a gravitational lensing theorem: the magnification of a source of uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A, where A is the area of the source and R_E and R_L are the Einstein radius and size of…

We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…

A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…

This paper derives the expressions of the multipole moments of an isolated gravitating source with an accuracy corresponding to the second post-Newtonian (2-PN) approximation of general relativity. The moments are obtained by a procedure of…

One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…

This paper investigates off-equatorial plane deflections and gravitational lensing of both null signals and massive particles in Kerr spacetime in the weak deflection limit, with the finite distance effect of the source and detector taken…

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…