相关论文: Two-mirror Schwarzschild aplanats. Basic relations
We investigate the observational signatures of an idealized double-ring and double-torus system orbiting a Schwarzschild black hole, allowing the two emitting components to have mutually inclined symmetry axes. Using general-relativistic…
Grazing incidence mirrors for X-ray astronomy are usually designed in the parabola-hyperbola (Wolter I) configuration. This design allows for optimal images on-axis, which however degrade rapidly with the off-axis angle. Mirror surfaces…
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the…
In the early 20th century, Laurent Schwartz observed that we can identify functions that extend smoothly to the point at infinity of one-point compactifications of Euclidean spaces. We show a similar result for a different compactification…
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…
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic…
In 1975, two papers were published that together sparked major new directions, conceptual, mathematical and practically applicable, in several previously disparate fields of science. In this short review, we expose key aspects of their…
The light distribution on the focal surface of spheric mirrors designed for telescopes in the lens-less Schmidt configuration is calculated analytically using geometrical optics. This analysis was motivated by considerations of the design…
Time delays are a key observable in strong gravitational lensing systems. Their theoretical expression is usually written as a sum of a geometrical delay and a Shapiro delay, with cosmology entering through angular diameter distances and a…
The utilization of a 6.5m monolithic primary mirror in a compact three-mirror anastigmat (TMA) telescope design offers unprecedented capabilities to accommodate various next generation science instruments. This design enables the rapid and…
The gravitational deflection effect of relativistic massive and massless particles up to the first post-Minkowskian order caused by a moving Schwarzschild black hole with a two-dimensional equatorial velocity, which contains the radial and…
Deflection of light by gravity was predicted by General Relativity and observationaly confirmed in 1919. In the following decades various aspects of the gravitational lens effect were explored theoretically, among them the possibility of…
We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing…
We propose a global minimal embedding of the Schwarzschild theory in a five-dimensional flat space by using two surfaces. Covariant field equations are deduced for the gravitational forces.
Certain semi-Riemannian metrics can be decomposed into a Riemannian part and an isochronal part. The properties of such metrics are particularly easy to visualize in a coordinate-free way, using isometric embedding. We present such an…
A modified version of the folded aplanatic Gregory telescope equipped with a spherical two-lens corrector is proposed for observations requiring a high signal-to-noise ratio. The basic telescope model has an aperture of 400 mm (f/3.0), its…
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…
In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which…
Hochschild two-cocycles play an important role in the deformation \`a la Gerstenhaber of associative algebras. The aim of this paper is to introduce the category of Hoch-algebras whose objects are associative algebras equipped with an extra…
We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness…