Related papers: Embedding spherical spacelike slices in a Schwarzs…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
We give a novel convergence theory for two-level hybrid Schwarz domain-decomposition (DD) methods for finite-element discretisations of the high-frequency Helmholtz equation. This theory gives sufficient conditions for the preconditioned…
The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion)…
We provide the first example of a geometric transition that resolves the Schwarzschild black hole into a smooth microstructure in eleven-dimensional supergravity on a seven-torus. The geometry is indistinguishable from a Schwarzschild black…
We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…
The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e. polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other…
One of the challenges of today's theoretical physics is to fully understand the connection between a geometrical object like area and a thermostatistical one like entropy, since area behaves analogously like entropy. The Bekenstein bound…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon. For a scalar potential containing a barrier, and using the most general…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by…
We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a…
We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area and total spherical curvature. These results can…
In a scalar-vector-gravity theory with the vector sector described by nonlinear electrodynamics, the field equations are integrated using the well-known gravitational decoupling method. The resulting spacetime corresponds to a spherically…