Related papers: The notes on thin shells

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of…

The Kerr-Schild (KS) geometry is linked tightly with the auxiliary \emph{flat} Minkowski background. Nevertheless, it describes many curved space-times and the related physical models, starting from cosmology and black holes to the…

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…

Thin shells in general relativity can be used both as models of collapsing objects and as probes in the space-time outside compact sources. Therefore they provide a useful tool for the analysis of the final fate of collapsing matter and of…

In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of…

We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form,…

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…

We investigate the gravitational fragmentation of expanding shells in the context of the linear thin--shell analysis. We make use of two very different numerical schemes; the FLASH Adaptive Mesh Refinement code and a version of the Benz…

In this paper, we obtain general conditions under which the wave equation is well-posed in spacetimes with metrics of Lipschitz regularity. In particular, the results can be applied to spacetimes where there is a loss of regularity on a…

This paper proves that, in a four-dimensional spherically symmetric spacetime manifold, one can consider coordinate transformations expressed by fractional linear maps which give rise to isometries and are the simplest example of coordinate…

The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…

We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime and the flat Friedmann-Robertson-Walker cosmology using the Israel thin-shell formalism. The joining of Taub and FRW spacetimes is reminiscent…

We study surface knots in 4-space by using generic planar projections. These projections have fold points and cusps as their singularities and the image of the singular point set divides the plane into several regions. The width (or the…

We study gravitational curvature effects in circular and radial geodesics in static, spherically symmetric space-times, using Fermi normal coordinates. We first set up these coordinates in the general case, and then use this to study…

We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…

We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the…

We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…

Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the…