Trapped surfaces in vacuum arising dynamically from mild incoming radiation

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 consequently show that the lower bound required to form a trapped surface can be relaxed. Second, we demonstrate that trapped surfaces form dynamically from a class of initial data which are large merely in a scaling-critical norm. This result is motivated in part by the scaling in Christodoulou's formation of trapped surfaces theorem for the Einstein-scalar field system in spherical symmetry

New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes

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 trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf map. The utility of this method is illustrated by providing marginally trapped surfaces crossing expanding and collapsing regions of a closed FLRW spacetime. The approach introduced in this paper is also extended to twisted spaces.Comment: 20 page

Trapped surfaces in cosmological spacetimes

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 surfaces may have matter density exceeding significantly the background matter density of the flat and homogeneous cosmological model.Comment: Revtex,12 pages, no diagram

The area of horizons and the trapped region

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 makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.Comment: 44 pages, v3: small changes in presentatio

Trapped surfaces and symmetries

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) symmetries and trapped submanifolds are also presented.Comment: 9 pages, no figures. Final corrected version to appear in Class. Quantum Gra

On the Definition of Averagely Trapped Surfaces

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 expansions be positive on average. A surface is averagely trapped in the latter sense if and only if its area $A$ and Hawking mass $M$ satisfy the isoperimetric inequality $16\pi M^2 > A$, with similar inequalities existing for other definitions of quasi-local energy.Comment: 4 page

Boost invariant marginally trapped surfaces in Minkowski 4-space

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invariant under the group of boost isometries. As an application, a proper star-surface is constructed.Comment: 13 pages, comment added in section