Related papers: Trapped Surfaces in Vacuum Spacetimes
The emergence of trapped surfaces in solutions to the Einstein field equations is intimately tied to the well-posedness properties of the corresponding Cauchy problem in the low regularity regime. In this paper, we study the question of…
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…
This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we…
We investigate existence and properties of trapped surfaces in two models of collapsing null dust shells within the Gibbons-Penrose construction. In the first model, the shell is initially a prolate spheroid, and the resulting singularity…
We investigate axially symmetric asymptotically flat vacuum self-gravitating system. A class of initial data with apparent horizon was numerically constructed. The examined solutions satisfy the Penrose inequality. The prior analysis of a…
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…
In this paper we show the existence of a large class of spherically symmetric data $d$ (on a spacelike hypersurface $S$), from which a perfect fluid spacetime (surrounded by vacuum) develops. This spacetime contains an event horizon (with…
This article gives necessary and sufficient conditions for the formation of trapped surfaces in spherically symmetric initial data defined on a closed manifold. Such trapped surfaces surround a region in which there occurs an enhancement of…
We present a rigorous proof of the Spacetime Penrose Inequality relating the ADM mass to the area of trapped surfaces in asymptotically flat initial data sets satisfying the dominant energy condition. The main theorem establishes that the…
In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
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 investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations. The problem is studied in the context of a characteristic initial value problem with data given on two null…
The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces…
We analyze how the hypotheses of Penrose's singularity theorem (1965) are modified by the action of disformal transformations (defined in terms of light-like vectors) upon a given space-time metric. In particular, we investigate the…
We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat everywhere else)…
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…
The classical Penrose inequality specifies a lower bound on the total mass in terms of the area of certain trapped surfaces. This fails at the semiclassical level. We conjecture a Quantum Penrose Inequality: the mass at spatial infinity is…