Related papers: Moser's Shadow Problem
We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked…
The Monotone Upper Bound Problem (Klee, 1965) asks if the number M(d,n) of vertices in a monotone path along edges of a d-dimensional polytope with n facets can be as large as conceivably possible: Is M(d,n) = M_{ubt}(d,n), the maximal…
We consider static black holes in Einstein gravity and study parameters characterizing the black hole size, namely the radii of the horizon $R_+$, photon sphere $R_{\rm ph}$ and black hole shadow $R_{\rm sh}$. We find a sequence of…
The apparent shadow of a black hole provides one of the most direct probes of strong-field general relativity. While the shadow size in asymptotically flat spacetimes is well understood, the influence of cosmic expansion on its apparent…
The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Amp\`ere equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and…
New mode in the hadron scattering is predicted to appear at the energies beyond $\sqrt{s}\simeq 2$ TeV: the antishadow scattering mode and the experiments at LHC and VLHC in hadronic reactions will be able to reveal it. The appearance of…
In this paper, the shadows cast by non-rotating and rotating modified gravity black holes are investigated. In addition to the black hole spin parameter $a$ and the inclination angle $\theta$ of observer, another parameter $\alpha$…
Given an unbounded strongly pseudoconvex domain D and a continuous real valued function h defined on bD, we study the existence of a (maximal) plurisubharmonic function u on D such that u=h on bD.
In this paper we extend to an infinite dimensional setting some results on the shadowing property that are known on finite dimensional compact manifolds without border and in $\mathbb{R}^n$. In fact, we show that if $\{\T(t):t\ge 0\}$ is a…
We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set, by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral…
The paper concerns the well-posedness and long-term asymptotics of growth--fragmentation equation with unbounded fragmentation rates and McKendrick--von Foerster boundary conditions. We provide three different methods of proving that there…
We compute the shadows of colliding black holes using the Kastor-Traschen cosmological multiblack hole solution that is an exact solution describing the collision of maximally charged black holes with a positive cosmological constant. We…
When the the shadow image of a supermassive black hole in the center of M87 was obtained a new era in the observational astrophysics began. The resolution improvement would allow to test extended gravity models at event horizon scales. We…
We prove a minimum degree version of the Kruskal--Katona theorem: given $d\ge 1/4$ and a triple system $F$ on $n$ vertices with minimum degree at least $d\binom n2$, we obtain asymptotically tight lower bounds for the size of its shadow.…
For a given bounded domain $\Omega\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as $t\to 0^+$. These…
The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference $d(n)$ between the largest and the smallest areas of the rectangles partitioning…
In the Einstein-bumblebee gravity, the Lorentz symmetry is spontaneously broken by a vector field. In this paper, we attempt to test the Lorentz symmetry via the observation of the shadow cast by the Kerr-like black hole with or without…
It is well known that the description of topological and geometric properties of bisectors in normed spaces is a non-trivial subject. In this paper we introduce the concept of bounded representation of bisectors in finite dimensional real…
This study explores the impact of antisymmetric tensor effects on spherically symmetric black holes, investigating photon spheres, shadows, emission rate and quasinormal frequencies in relation to a parameter which triggers the Lorentz…
It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for…