Related papers: A trapped surface in the higher-dimensional self-s…
The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question whether closed trapped surfaces can…
Marginally trapped surfaces (MTSs) are commonly used in numerical relativity to locate black holes. For dynamical black holes, it is not known generally if this procedure is sufficiently reliable. Even for Schwarzschild black holes, Wald…
We review the basic definitions and properties of trapped surfaces and discuss them in the context of Kerr-Vaidya line-element. Our study shows that the apparent horizon does not exist in general for axisymmetric space-times. The reason…
It is proven that in Vaidya spacetimes of bounded total mass, the outer boundary, in spacetime, of the region containing outer trapped surfaces, is the event horizon. Further, it is shown that the region containing trapped surfaces in these…
The boundary of the region in spacetime containing future-trapped closed surfaces is considered. In asymptotically flat spacetimes, this boundary does not need to be the event horizon nor a dynamical/trapping horizon. Some properties of…
We present some simple pen and paper examples of trapped surfaces in order to help visualising this key concept of the theory of gravitational collapse. We collect these examples from time-symmetric initial data, 2+1 dimensions, collapsing…
Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By…
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…
We discuss the boundary of the spacetime region through each point of which a trapped surface passes, first in some simple soluble examples, and then in the self-similar Vaidya solution. For the latter the boundary must lie strictly inside…
The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic…
We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial…
We investigate the end state of gravitational collapse of null fluid in higher dimensional space-times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. The naked singularity spectrum in…
This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…
We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space.…
A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de…
We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized)…
The concept of a marginally trapped surface is important in the theory of general relativity. In the Schwarzschild black hole spacetime, its event horizon is foliated by marginally trapped surfaces. In a more general black hole spacetime,…
We investigate existence and properties of trapped surfaces in two models of collapsing null dust shells within the Gibbons-Penrose construction. In the first model, the shell is initially a prolate spheroid, and the resulting singularity…
A unifying definition of trapped submanifold for arbitrary codimension by means of its mean curvature vector is presented. Then, the interplay between (generalized) symmetries and trapped submanifolds is studied, proving in particular that…