Related papers: Moser's Shadow Problem
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with…
For n >= 2 a construction is given for a large family of compact convex sets K and L in n-dimensional Euclidean space such that the orthogonal projection L_u onto the subspace u^\perp contains a translate of the corresponding projection K_u…
We studied the shadow cast by a rotating Bardeen black hole within the framework of asymptotically safe gravity. The null geodesics were analyzed using the Hamilton Jacobi separation method to derive shadow observables. Our findings show…
The Monotone Upper Bound Problem asks for the maximal number M(d,n) of vertices on a strictly-increasing edge-path on a simple d-polytope with n facets. More specifically, it asks whether the upper bound M(d,n)<=M_{ubt}(d,n) provided by…
Motivated by recent work on rotating black hole shadow [Phys. Rev. D101, 084029 (2020)], we investigate the shadow behaviors of rotating Hayward-de Sitter black hole for static observers at a finite distance in terms of astronomical…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
Motivated by recent work on the Modified Maxwell (ModMax) black holes [Phys.Lett.B 10.1016/j.physletb.2020.136011], which are invariant in duality rotations and conformal transformations founded in [ Phys.Rev.D 10.1103/PhysRevD.102.121703],…
A stellar occultation by a trans-Neptunian object (TNO) provides an opportunity to probe its size and shape. Very few occultations by TNOs have been sampled simultaneously from multiple locations, while a robust estimation of shadow size…
Define a body A to be able to hide behind a body B if the orthogonal projection of B contains a translation of the corresponding orthogonal projection of A in every direction. In two dimensions, it is easy to observe that there exist two…
Combining a modular approach to the $abc$ conjecture developed by the second author with the classical method of linear forms in logarithms, we obtain improved unconditional bounds for two classical problems. First, for Szpiro's conjecture…
We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime…
For a given natural number $n$, the second part of Hilbert's 16th Problem asks whether there exists a finite upper bound for the maximum number of limit cycles that planar polynomial vector fields of degree $n$ can have. This maximum number…
The shadows cast by non-rotating and rotating modified gravity (MOG) black holes are determined by the two parameters mass $M$ and angular momentum $J=Ma$. The sizes of the shadows cast by the spherically symmetric static Schwarzschild-MOG…
The scattering of a positron by a muon in the presence of a linearly polarized laser field is investigated in the first Born approximation. The theoretical results reveals: 1) at large scattering angle, an amount of multiphoton processes…
We study the size of the shadow of $k$-uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a function of the degree bound and $k$. We show that cliques are…
In the gravitation n-body Problem, a homothetic orbit is a special solution of the Newton's Equations of motion, in which each body moves along a straight line through the center of mass and forming at any time a central configuration. In…
The apparent angular size of the shadow of a black hole in an expanding Universe is redshift-dependent. Since cosmological redshifts change with time - known as the redshift drift - all redshift-dependent quantities acquire a…
We prove a Bernstein-von Mises theorem for a general class of high dimensional nonlinear Bayesian inverse problems in the vanishing noise limit. We propose a sufficient condition on the growth rate of the number of unknown parameters under…
We consider a black hole mimicker given by an exact solution of the stationary and axially symmetric field equations in vacuum known as the $\delta$-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion…
We develop a fully numerical framework to compute and visualize the \emph{hypershadow}\cite{Novo:2024wyn}, the three-dimensional generalization of the black hole shadow in five-dimensional spacetimes. Our method is based on backward ray…