相关论文: Geometry of crossing null shells

Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion…

The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…

Applying the distributional formalism to study the dynamics of thin shells in general relativity, we regain the junction equations for matching of two spherically symmetric spacetimes separated by a singular hypersurface. In particular, we…

Within the framework of mode-coupling theory, the glass-transition scenario is investigated for a system of particles interacting with a hard-core repulsion and an additional square-shoulder soft core at larger distances. The static…

Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM)…

In recent years, it has been rather fashionable to talk about geometric trinity of gravity. The main idea is that one can formally present the gravity equations in different terms, those of either torsion or nonmetricity instead of…

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…

Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large number of results in algebraic geometry, particular on birational geometry of moduli spaces. We illustrate some of the methods behind these result…

Spectral flow in two-dimensional field theories is known to correspond to geometrical twisting between two circles in the gravity dual. We generalize this operation to the geometries which have SO(k+1) x SO(k+1) isometries with k>1 and…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…

This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…

We present a definition of null G-structures on Lorentzian manifolds and investigate their geometric properties. This definition includes the Robinson structure on 4-dimensional black holes as well as the null structures that appear in all…

We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and…

In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…

In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter…

This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in a liquid in any orientation. Despite recent results of F. Wegner pointing towards an affirmative answer, a…

Understanding the velocity field is very important for modern cosmology: it gives insights to structure formation in general, and also its properties are crucial ingredients in modelling redshift-space distortions and in interpreting…

We introduce the notion of domains with uniform squeezing property, study various analytic and geometric properties of such domains and show that they cover many interesting examples, including Teichmuller spaces and Hermitian symmetric…

Building on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and highlight the emergent nature of gravity, we demonstrate its robustness in a broader context. Using the same entropy density, we show…