Related papers: Geometrical joke(r?)s for SETI
Cross-sections for particles scattered from selected spatial geometries exhibit many of the same interesting features as Mie scattering.
We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti)…
Classical geometry of de Sitter spacetime is reviewed in arbitrary dimensions. Topics include coordinate systems, geodesic motions, and Penrose diagrams with detailed calculations.
The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output…
Configurations of masses located at the vertices of Platonic solids deep within the bulk of de Sitter spacetime generate deformations of the cosmological horizon with the geometry dual to these polyhedra. The horizon data encodes both the…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
This survey contains a recollection of results, problems and conversations which go back to the early years of Representation Theory and Tilting Theory.
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We generalize the superposition principle for time-symmetric initial data of black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue problem $\Delta_g\phi={1/8}(R_g-2\Lambda)\phi$ for a conformal scale $\phi$ applied…
The recently discussed notion of geometric entropy is shown to be related to earlier calculations of thermal effects in Rindler space. The evaluation is extended to de Sitter space and to a two-dimensional black hole.
The Kadomtsev-Petviiashvili equation is considered as a mathematical caricature of large and rogue waves.
A conjecture regarding the structure of expander graphs is discussed.
See hep-th/9903228.
A few thoughts on physical meaning of geometry, space and time.
We briefly review the evidence that anti-de Sitter spacetime is nonlinearly unstable, and the perturbative arguments that there should exist geons - nonsingular solutions to Einstein's equation with a helical symmetry. We then explicitly…
In this paper, we investigate the fully relativistic time delay of pulsar signals propagating in the vicinity of a rotating black hole and its potential mimickers, including a deformed Kerr black hole and the Janis-Newman-Winicour naked…
Some aspects of multidimensional soliton geometry are considered.
This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems continue to be influential in computational geometry and in…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and…