Related papers: Remarks on the size of apparent horizons
This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof…
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…
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…
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…
We consider the application of stable marginally outer trapped surfaces to problems concerning the size of material bodies and the area of black holes. The results presented extend to general initial data sets (V,g,K) previous results…
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…
This article introduces the subject of quasi-local horizons at a level suitable for physics graduate students who have taken a first course on general relativity. It reviews properties of trapped surfaces and trapped regions in some simple…
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…
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…
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…
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…
Black holes in general relativity are characterized by their trapping horizon, a one-way membrane that can be crossed only inwards. The existence of trapping horizons in astrophysical black holes can be tested observationally using a…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any…
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…
We consider an initial data set having a continuous symmetry and a marginally outer trapped surface (MOTS) that is not preserved by this symmetry. We show that such a MOTS is unstable except in an exceptional case. In non-rotating cases we…
We establish sufficient conditions for the appearance of apparent horizons in spherically symmetric initial data when spacetime is foliated extrinsically. Let $M$ and $P$ be respectively the total material energy and the total material…
In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by $4\pi/c$,…
We prove that the boundary of the trapped region in an asymptotically Euclidean Riemannian manifold of dimension at least 3 is a stable smooth minimal hypersurface except for a singular set of codimension at least 8.
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…
A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract…