Related papers: Shadow geometry at singular points of CAT(k) space…
Some aspects of lightlike dimensional reduction in flat spacetime are studied with emphasis to classical applications. Among them the Galilean transformation of shadows induced by inertial frame changes is studied in detail by proving that,…
Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it fixes a point.
For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space,…
Automatic detection of shadow regions in an image is a difficult task due to the lack of prior information about the illumination source and the dynamic of the scene objects. To address this problem, in this paper, a deep-learning based…
We consider a simple model of a black hole surrounded by a toroidal structure and experiencing deformation due to magnetic field and the tidal force. For this system we construct the shadows of Preston-Poisson black hole, apply it to…
It is now known that the shadow is not only the property of a black hole, it can also be cast by other compact objects like naked singularities. However, there exist some novel features of the shadow of the naked singularities which are…
We study a special type of shadowing (DSP) of chain transitive continuous self-maps of compact Hausdorff spaces. We prove some basic properties of DSP. As application of DSP, we obtain sufficient conditions for a statistical variant of…
In this work, we study the optical properties of a class of magnetically charged rotating black hole spacetimes. The black holes in question are assumed to be immersed in the quintessence field, and subsequently, the resulting black hole…
The shadow of a rotating black hole with nonvanishing gravitomagnetic charge has been studied. It was shown that in addition to the angular momentum of black hole the gravitomagnetic charge term deforms the shape of the black hole shadow.…
Given a submanifold $M\subset \mathbf{R}^\nu$, a curve $\gamma:I\to M$ and tangent vectors $v$ along $\gamma$, we roll the tangent space along $\gamma$. In doing so, we get an imprint/trace of $\gamma$ on the tangent space, as well as an…
By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our…
A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector…
Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…
Direct imaging of supermassive black holes (SMBHs) at event horizon scale resolutions, as recently done by the Event Horizon Telescope, allows for testing alternative models to SMBHs such as Kerr naked singularities (KNSs). We demonstrate…
Using the Hamilton-Jacobi method, we study certain optical shadows of rotating Bardeen-AdS black holes in the presence of internal and external field contributions. Precisely, we examine the shadow using one-dimensional real curves. By…
We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. By showing that the formalism of measurement frames offers a natural framework for shadow tomography --…
The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that…
We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic…
We show that, away from the axis of symmetry, no continuous degeneration exists between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore, except possibly for…
The relation between the black hole shadow and the black hole thermodynamics is investigated. We find that the phase structure can be reflected by the shadow radius for the spherically symmetric black hole. We also find that the shadow size…