Related papers: Connection between horizons and algebraic type
We introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of $E_6$. This variety is intricately related with many other moduli…
The main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non-compact K\"ahler manifold of finite volume with reasonable geometric assumptions to its universal covering. Applicable examples…
Heckenberger introduced the Weyl groupoid of a finite-dimensional Nichols algebra of diagonal type. We replace the matrix of its braiding by a higher tensor and present a construction which yields further Weyl groupoids. Abelian cohomology…
We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations,…
We investigated the relation between the behavior of gravitational wave at late time and the limit structure of future null infinity tangent which will determine the topology of the event horizon far in the future. In the present article,…
The vorticity statistics characterises both the direct and the inverse turbulent cascades of two-dimensional fluid flows. The fluid/gravity correspondence relates fluid flows to black brane dynamics. We construct the holographic vorticity…
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
We establish a correspondence between the gravitational phase space at null infinity and the subleading phase space near a finite-distance null hypersurface, such as a black hole horizon. Within this framework, we identify the celestial…
We prove trapped-surface formation for the Einstein-Weyl spinor system (gravity coupled to a massless left-handed two-spinor) without any symmetry assumption. To this end we establish a semi-global solution under double null foliation and…
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned…
Necessary conditions for various algebraic types of the Weyl tensor are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically…
We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the…
We explore the realization of distinct analog black hole horizons within tilted Weyl semimetals by comparing two models with contrasting spectral properties. We demonstrate that a spatially varying tilt in the Weyl cone structure creates an…
3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green's functions parametrized by a 16 element matrix $e^\mu_\alpha$ in an expansion around the Weyl point. The matrix $e^{\mu}_{\alpha}$ can…
We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…
In this work we analyse asymptotically flat, spherically symmetric spacetimes in which an event horizon is present without any trapped surfaces. We identify two types of such spacetimes, each related to the asymptotic behaviour (in time) of…
The theory of non-expanding horizons (NEH) geometry and the theory of near horizon geometries (NHG) are two mathematical relativity frameworks generalizing the black hole theory. From the point of view of the NEHs theory, a NHG is just a…
A $Z_3$-graded Hopf algebra structure of exterior algebra with two generators is introduced. Two covariant differential calculus on the $Z_3$-graded exterior algebra are presented. Using the generators and their partial derivatives a…
We study the behavior of spatially homogeneous brane-worlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these brane-worlds can be locally either isotropic or…