Related papers: Moser's Shadow Problem
Stupendously large astrophysical black holes (SLABs) are hypothetical black holes with masses of more than a trillion Suns. Because observable consequences of their existence have only recently been seriously considered, there have been…
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…
Let $f\colon X\to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is onto. Using this we go on to show that, for expansive…
The $\gamma$-metric is a static, axially-symmetric singular solution of the vacuum Einstein's equations without an event horizon. This is a two-parameter family of solutions, generic values of one of which (called $\gamma$) measure the…
Black hole (BH) shadows in dynamical binary BHs (BBHs) have been produced via ray-tracing techniques on top of expensive fully non-linear numerical relativity simulations. We show that the main features of these shadows are captured by a…
We investigate the constraints that Olbers Paradox, applied to the Zodiacal Background as measured from space, sets on outer solar system objects. If extended to very faint limits, R = 40--50 mag, the steep optical luminosity function (LF)…
We investigate the shadow cast by a sort of new regular black holes which are characterized by an asymptotically Minkowski core and the Sub-Planckian curvature. Firstly, we extend the metric with spherical symmetry to the one of rotating…
We study the following nonlinear elliptic problem [-\Delta u =F^{'} (u) in {\mathbb R}^n] where $F(u)$ is a periodic function. Moser (1986) showed that for any minimal and nonself-intersecting solution, there exist $ \alpha \in {\mathbb…
We study the shadows of four dimensional black holes in M-theory inspired models. We first inspect the influence of M2-branes on such optical aspects for non-rotating solutions. In particular, we show that the M2-brane number can control…
We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed density function $f$ that affects how area and perimeter are measured. We examine density functions that are symmetric, radially increasing, and satisfy two additional…
A good range of problems on trees can be described by the following general setting: Given a bilinear map $*:\mathbb R^d\times\mathbb R^d\to\mathbb R^d$ and a vector $s\in\mathbb R^d$, we need to estimate the largest possible absolute value…
For a bilinear map $*:\mathbb R^d\times \mathbb R^d\to \mathbb R^d$ of nonnegative coefficients and a vector $s\in \mathbb R^d$ of positive entries, among an exponentially number of ways combining $n$ instances of $s$ using $n-1$…
We compute the Morse index of nodal radial solutions to the H\'enon problem \[\left\{\begin{array}{ll} -\Delta u = |x|^{\alpha}|u|^{p-1} u \qquad & \text{ in } B, \newline u= 0 & \text{ on } \partial B, \end{array} \right. \] where $B$…
A model based on the hadronic fluctuations of the real photon is developed to describe the total photonucleon and photonuclear cross sections in the energy region above the nucleon resonances. The hadronic spectral function of the photon is…
Horn's problem is concerned with characterizing the eigenvalues $(a,b,c)$ of Hermitian matrices $(A,B,C)$ satisfying the constraint $A+B=C$ and forming the edges of a triangle in the space of Hermitian matrices. It has deep connections to…
In light of the Event Horizon Telescope (EHT) images of the supermassive black holes $\textrm{Sgr A}^\star$ and $\textrm{M87}^\star$, we explore a potential supersymmetry suspicion within the observational data. Specifically, we investigate…
In this paper, we study the shadow of a 4D Einstein-Gauss-Bonnet black hole as photons couple to the Weyl tensor and find that the propagation of light depends on its polarization which leads to the existence of a double shadow. Then, we…
The first images of black hole shadows open new possibilities to constrain modern extended gravity theories. We present the method of shadow background calculation for black hole solutions in the form of Taylor series where $g_{11} = -…
The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width. It is known that a maximal area shape exists, and that its area is at least…