Related papers: Lower bound on the compactness of isotropic ultra-…
We investigate the geodesic structure and optical appearance of compact objects with primary scalar hair in shift- and parity-symmetric beyond Horndeski gravity. The analytic solution considered here depends on a theory parameter and a…
Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…
We have provided here a new class of interior solutions for anisotropic stars admitting conformal motion in higher dimensional noncommutative spacetime. The Einstein fields equations are solved by choosing a particular density distribution…
This paper aims to show the possibility of the existence of super-massive compact objects with radii less than the Schwarzschild one, which is one of the principal consequences of the author's geodesic-invariant gravitation equations (Ann.…
We study observational signatures of nonsingular ultracompact objects regularized by nonlinear electrodynamics. The phenomenon of birefringence causes photons of different polarizations to propagate with respect to two distinct metrics,…
We construct new supersymmetric multi-black ring solutions on the Eguchi-Hanson base space as solutions of the five-dimensional minimal supergravity. The space-time has an asymptotically locally Euclidean time slice, i.e., it has the…
We show that the space of min-max minimal hypersurfaces is non-compact when the manifold has an analytic metric of positive Ricci curvature and dimension $3\leq n+1\leq 7$. Furthermore, we show that bumpy metrics with positive Ricci…
We provide, for any $r\in (0,1)$, lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius $1$ and $r$. The lower bounds are mostly folk, but the upper bounds improve the best previously known…
Motivated by a recently discovered connection between the greybody factors of black holes and the ringdown signal, we investigate the greybody factors of ultracompact horizonless objects, also elucidating their connection to echoes. The…
To what extent are all astrophysical, dark, compact objects both black holes (BHs) and described by the Kerr geometry? We embark on the exercise of defying the universality of this remarkable idea, often called the "Kerr hypothesis". After…
The generic properties of compact objects made of two different fluids of dark matter are studied in a scale invariant approach. We investigate compact objects with a core-shell structure, where the two fluids are separated, and with mixed…
We discuss the relic density of the lightest of the supersymmetric particles ({\small LSP}) in view of new cosmological data, which favour the concept of an accelerating Universe with a non-vanishing cosmological constant. The new bound on…
We classify irreducible representations of compact connected Lie groups whose orbit space is isometric to the orbit space of a representation of a compact Lie group of dimension~$7$, $8$ or $9$. They turn out to be closely related to…
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
It has recently been proved that, for constant density stars, there is a critical value $\Lambda^{*}=1$ for the dimensionless density parameter $\Lambda\equiv 4\pi R^2\rho_{\text{max}}$ of the star above which the asymptotically measured…
Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in…
Isotropic scattering in various spatial dimensions is considered for arbitrary finite-range potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire,…
We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only…
Consider a compact K\"{a}hler manifold $M^m$ with Ricci curvature lower bound $Ric_M\geq -2(m+1) .$ Assume that its universal cover $% \widetilde{M}$ has maximal bottom of spectrum $\lambda_1(\widetilde{M}%) =m^2.$ Then we prove that…