Related papers: Trapped surfaces and spherical closed cosmologies
Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic…
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…
We continue the investigation of formation of trapped surfaces in strongly curved , conformally flat geometries. Initial data in quasi-polar gauges rather then maximal ones are considered. This implies that apparent horizons coincide with…
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…
Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an…
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…
In this paper, we study the "minimal requirement" on the incoming radiation that guarantees a trapped surface to form in vacuum. First, we extend the region of existence in Christodoulou's theorem on the formation of trapped surfaces and…
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and…
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…
The existence of closed trapped surfaces need not imply a cosmological singularity when the spatial hypersurfaces are compact. This is illustrated by a variety of examples, in particular de Sitter spacetime admits many closed trapped…
Previously suggested definitions of averagely trapped surfaces are not well-defined properties of 2-surfaces, and can include surfaces in flat space-time. A natural definition of averagely trapped surfaces is that the product of the null…
We consider the formation of trapped surfaces in the evolution of the Einstein-scalar field system without symmetries. To this end, we follow An's strategy to analyse the formation of trapped surfaces in vacuum and for the Einstein-Maxwell…
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…
An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric…
In this paper, we examine gravitational collapse of matter fields in $n$-dimensional general relativity. The matter energy-momentum tensor under consideration includes dust, perfect fluids with equations of state and matter admitting bulk…
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)…
We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This,…
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…
In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally…