Related papers: On the mechanism of trapped surface formation
We analytically construct an infinite number of trapped toroids in spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus on initial data which represent "constant density stars" momentarily at rest. There exists an…
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…
Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…
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…
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…
This paper deals with a detail study of gravitational collapse of dust and viscous fluids under the assumptions of spherical symmetry. Our main goal is to closely analyze the horizons which arise during this gravitational phenomenon. To…
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 investigate the relationship between the star formation rate per unit area and the surface density of the ISM (the local Kennicutt-Schmitt law) using a simplified model of the ISM and a simple estimate of the star formation rate based on…
Most fully developed galaxies have a vivid spiral structure, but the formation and evolution of the spiral structure are still an enigma in astrophysics. In this paper, according to the standard Newtonian gravitational theory and some…
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…
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…
A static, spherically symmetric spacetime with negative pressures is conjectured inside a star. The gravitational field is repulsive and so a central singularity is avoided. The positive energy density and the pressures of the imperfect…
We study global star formation thresholds in the outer parts of galaxies by investigating the stability of disk galaxies embedded in dark halos. The disks are self-gravitating, contain metals and dust, and are exposed to UV radiation. We…
We compile observations of the surface mass density profiles of dense stellar systems, including globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals…
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…
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…
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random…
We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the…
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…