Related papers: A Lighthouse Illumination Problem
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We…
Whether the spiral structure of galaxies is trailing or leading has been a subject of debate. We present a new spin parity catalog of 146 spiral galaxies that lists the following three pieces of information: whether the spiral structure…
The deflection angle of a light ray can be arbitrarily large near a light sphere. The time-symmetrical shape of light curves of a pair of light rays reflected by a light sphere of a lens object does not depend on the details of the lens…
In his classical work, W. Blaschke proved that a convex body whose shadow boundaries are flat for every direction of parallel illumination must be an ellipsoid. An extension recently proposed by I. Gonzalez-Garc\'ia, J. Jer\'onimo-Castro,…
Most galaxies host central supermassive black holes. As two galaxies merge, the black holes also merge. The final single black hole may suffer a kick due to asymmetric gravitational radiation and may not be at the centre of the galaxy;…
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze…
The luminosity variation of a stellar source due to the gravitational microlensing effect can be considered also if the light rays are defocused (instead of focused) toward the observer. In this case, we should detect a gap instead of a…
A well-known object in classical Euclidean geometry is the circumcenter of a triangle, i.e., the point that is equidistant from all vertices. The purpose of this paper is to provide a systematic study of the circumcenter of sets containing…
It has been established that Black Hole (BH) spacetimes obeying some general set of assumptions always possess, at least, one light ring (per rotation sense) [arXiv:2003.06445]. This theorem was originally established for asymptotically…
A generalization of the Majumdar-Papapetrou multi-black hole spacetime was recently constructed by Teo and Wan [1], describing charged and spinning (extremal) balanced black holes in asymptotically flat spacetime. We explore the dynamics of…
With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is,…
Lights Out! is a game played on a $5 \times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration…
A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…
The convex hull of a ball with an exterior point is called a spike (or cap). A union of finitely many spikes of a ball is called a spiky ball. If a spiky ball is convex, then we call it a cap body. In this note we upper bound the…
The CAIRNS (Cluster And Infall Region Nearby Survey) project is a large spectroscopic survey of the infall regions surrounding nine nearby rich clusters of galaxies. I describe the survey and use the kinematics of galaxies in the infall…
The orientations of brightest cluster galaxies (BCGs) and their host clusters tend to be aligned, but the mechanism driving this is not clear. To probe the role of cluster mergers in this process, we quantify alignments of 38 BCGs in 22…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
The geometry of black hole spacetimes can be probed with exquisite precision in the gravitational-wave window, and possibly also in the optical regime. We study the accretion of bright spots -- objects which emit strongly in the optical or…
If identical photons meet at a semi-transparent mirror they appear to leave in the same direction, an effect called "two-photon interference". It has been known for some time that this effect should occur for photons generated by dissimilar…