Related papers: Shadow geometry at singular points of CAT(k) space…
We obtain the shadow cast induced by the rotating black hole with an anisotropic matter. A Killing tensor representing the hidden symmetry is derived explicitly. The existence of separability structure implies a complete integrability of…
A brief illustrative discussion of the shadows of black holes at local and cosmological distances is presented. Starting from definition of the term and discussion of recent observations, we then investigate shadows at large, cosmological…
The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it existed for all time. Here we ask the question of how this shadow comes about in the…
There were obtained some properties of weakly m-convex sets. Various kinds of the problem of shadow were investigated. There was obtained the lower estimation for the number of balls that are necessary to create a shadow at the point of the…
We construct a subset $A$ of the unit disc with the following properties. (i) The set $A$ is the finite union of disjoint line segments. (ii) The shadow of $A$ is arbitrarily close to the shadow of the unit disc in "most" directions. (iii)…
Light bending by the strong gravity around the black hole will form the so-called black hole shadow, the shape of which can shed light on the structure of the near-horizon geometry to possibly reveal novel physics of strong gravity and…
For a continuous self-map of a compact metric space, we provide a sufficient condition for the orbit of a point to converge to a periodic orbit or an odometer. We show that if a continuous self-map of a compact metric space has the…
Shadows encode rich information about scene geometry and illumination, yet existing methods either predict a unified shadow mask or overlook attached shadows entirely. We address this gap by proposing a framework for jointly detecting cast…
In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…
Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…
Due to the acceleration of the black hole, the circular orbits of the photons will deviate from the equatorial plane and the property of the black hole shadow will change. We find that the latitude of the circular orbit increases with the…
A beyond Horndeski theory is considered that admits wormholes, black holes and naked singularities. In this theory the shadow images of the black holes and the exotic compact objects (ECOs), illuminated by an optically and geometrically…
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…
In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope l with the horizontal plane. Depending on the value of l…
Cosmic expansion is expected to influence on the size of black hole shadow observed by comoving observer. Except the simplest case of Schwarzschild black hole in de Sitter universe, analytical approach for calculation of shadow size in…
The shadow of a black hole can be one of the strong observational evidences for stationary black holes. If we see shadows at the center of galaxies, we would say whether the observed compact objects are black holes. In this paper, we…
We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex method for linear programming among other applications. We prove…
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…