Related papers: Trapped surfaces in spherical expanding open unive…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
We introduce the concept of $k-$future convex spacelike/null hypersurface $\Sigma$ in an $n+1$ dimensional spacetime $M$ and prove that no $k-$dimensional closed trapped submanifold (k-CTM) can be tangent to $\Sigma$ from its future side.…
In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical…
We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are…
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 the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…
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…
Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…
The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is…
Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…
We consider here the existence and structure of trapped surfaces, horizons and singularities in spherically symmetric static massless scalar field spacetimes. Earlier studies have shown that there exists no event horizon in such spacetimes…
Motivated by the question of how generic inflation is, I study the time-evolution of topological surfaces in an inhomogeneous cosmology with positive cosmological constant $\Lambda$. If matter fields satisfy the Weak Energy Condition,…
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 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…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
It is standard assertion in relativity that, subject to an energy condition and the cosmic censorship hypothesis, closed trapped surfaces are not visible from future null infinity. A proof given by Hawking & Ellis in ''The Large Scale…
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,…
One signature of an expanding universe is the time-variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments…
In the Friedmann equations, an infinite initial density is avoided only when the universe is spatially flat. With such equations being then valid when the scale factor $a=0$, the universe must also be in the state of vacuum when $a$ is…
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…