Related papers: Involute, minimal, outer and increasingly trapped …
Seven different refinements of trapped surfaces are proposed, each intended as potential stability conditions. This article concerns spherical symmetry, but each condition can be generalized. Involute trapped spheres satisfy a similar…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
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…
I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay…
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…
Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally…
Further to our consideration on trapped surfaces in gravitational collapse, where pressures were allowed to be negative while satisfying weak energy condition to avoid trapped surface formation, we discuss here several other attempts of…
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
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…
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a…
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 study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible…
I will discuss some recent results on marginally outer trapped surfaces, apparent horizons, and the trapped region. A couple of applications of the results developed for marginally outer trapped surfaces to coalescence of black holes and to…
A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces…
We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…
A very simple criterion to ascertain if (D-2)-surfaces are trapped in arbitrary D-dimensional Lorentzian manifolds is given. The result is purely geometric, independent of the particular gravitational theory, of any field equations or of…
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…
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…
We discuss a family of inequalities involving the area, angular momentum and charges of stably outermost marginally trapped surfaces in generic non-vacuum dynamical spacetimes, with non-negative cosmological constant and matter sources…