Related papers: Angular distances in metric theories
In order to clarify effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss-Bonnet (GB) theorem in differential geometry…
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These…
An analytical solution for the light trajectory in the near-zone of the gravitational field of one pointlike body in arbitrary slow-motion in the post-post-Newtonian approximation is presented in harmonic gauge. Expressions for total light…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
For paraxial and non-paraxial light, numerous measures of electromagnetic attribute are expressible in terms of photon annihilation and creation. Accordingly, energy, angular momentum and chirality measures acquire a consistent…
We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In…
In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly…
A precise modeling of light trajectories in the solar system on the sub-micro-arcsecond and nano-arcsecond scale of accuracy requires the metric tensor of solar system bodies in post-linear approximation. The Multipolar Post-Minkowskian…
By using a method improved with a generalized optical metric, the deflection of light for an observer and source at finite distance from a lens object in a stationary, axisymmetric and asymptotically flat spacetime has been recently…
After discussing some subtle issues concerning the computation of deflection angle, a general but simple expression of bending angle of light rays in weak deflection limit has been presented for a general static and spherically symmetric…
The angular momentum of radiation from an arbitrarily moving relativistic charge is studied. The angular momentum is presented as the sum of the angular momentum relative to the point where the charge is located at a retarded moment of time…
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of…
In the context of earlier work, we investigate the emergence of a "distance" in the physical world. For this we consider a Cantor ternary like process, but much more general: properties like perfectness and disconnectedness are not invoked,…
We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…
Light does not travel in a perfectly straight line when it passes near massive objects. In this work, we calculate the gravitational deflection of light using the gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)],…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
The gravitational metric tensor implies a variable dielectric tensor of vacuum around gravitational matter. The curved spacetime in general relativity is then associated with a polarizable vacuum. It is found that the number density of the…
This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in…
Gravitational light deflection is known as one of three classical tests of general relativity and the angle of deflection may be computed explicitly using approximate or exact solutions describing the gravitational force generated from a…