Related papers: Some examples of trapped surfaces
A recently proposed approach to the construction of the Vaidya metric in double-null coordinates for generic mass functions is extended to the $n$-dimensional $(n>2)$ case and to allow the inclusion of a cosmological constant. The approach…
In this work, we consider a semiclassical description of the spherically symmetric gravitational collapse with a massless scalar field. In particular, we employ an effective scenario provided by holonomy corrections from loop quantum…
Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to…
It was recently shown that a massive thin shell that is sandwiched between a flat interior and an exterior geometry given by the outgoing Vaidya metric becomes null in a finite proper time. We investigate this transition for a general…
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken…
We perform simulations in a simple model that aims to mimic the hydrodynamic evolution of a relativistic fluid during a cosmological first-order phase transitions. The observable we are concerned with is hereby the spectrum of gravitational…
Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained…
We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy…
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a…
Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…
Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden…
The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles,…
We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame,…
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that, from the point of view of any timelike observer outside of such a black hole, trapping can be…
We consider here the existence and structure of trapped surfaces, horizons and singularities in spherically symmetric static massless scalar field spacetimes. Earlier studies have shown that there exists no event horizon in such spacetimes…
The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of…
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite…