Related papers: Generic Spectrahedral Shadows
We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show that if the curve is smooth and defined over the rational…
Generalized diagonal matrices are matrices that have two ladders of entries that are zero in the upper right and bottom left corners. The minors of generic generalized diagonal matrices have square-free initial ideals. We give a description…
It is now known that, apart from black holes, some naked singularities can also cast shadows which provide their possible observable signatures. We examine the relevant question here as to how to distinguish then these entities from each…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
We study the cone of non-negative polynomials on generalized elliptic curves. We show that the zero set of every extreme ray has dense real points. If a generalized elliptic curve is embedded via a complete linear system, then we show that…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
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…
Supersymmetric black ring solutions of five dimensional supergravity coupled to an arbitrary number of vector multiplets are constructed. The solutions are asymptotically flat and describe configurations of concentric black rings which have…
Regular black hole is one of the bottom-up solutions designed to eliminate the singularity at the center of black holes. Its horizonless solution has gained interest recently to model ultracompact star. Despite interesting, this proposal is…
The compact dark objects with very large masses residing at the centres of galaxies are believed to be black holes. Due to the gravitational lensing effect, they would cast a shadow larger than their horizon size over the background, whose…
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set…
Skeletal polyhedra are discrete structures made up of finite, flat or skew, or infinite, helical or zigzag, polygons as faces, with two faces on each edge and a circular vertex-figure at each vertex. When a variant of Wythoff's construction…
We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.
We investigate the shadow properties of a wide class of spacetimes arising from different parameter regimes of the generalized Hayward metric, characterized by two independent parameters $(\sigma, \kappa)$ (Phys. Rev. D 106, 044028). This…
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…
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve…
A matrix polynomial is a polynomial in a complex variable $\lambda$ with coefficients in $n \times n$ complex matrices. The spectral curve of a matrix polynomial $P(\lambda)$ is the curve $\{ (\lambda, \mu) \in \mathbb{C}^2 \mid…
The problem of bending and scattering of light rays passing outside from the entrance to a wormhole with zero gravitational mass is considered. The process of ray capture by a wormhole as well as the process of formation of a shadow when…
We explore the shadow of certain class generalized Kerr black holes, which are non vacuum solutions of the Einstein equations with exotic matter. The images depend on the angular momentum of the compact object, the characteristic parameter…
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)…