Trapped surfaces and spherical closed cosmologies

Abstract

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 matter over the average. The conditions are posed directly in terms of physical variables and show that what one needs is a relatively large amount of excess matter confined to a small volume. The expansion of the universe and an outward flow of matter oppose the formation of trapped surfaces; an inward flow of matter helps. The model can be regarded as a Friedmann-Lema\^ıtre-Walker cosmology with localized spherical inhomogeneities. We show that the total excess mass cannot be too large.

36 pages

Cited by in corpus (15)

• Optical scalars in spherical spacetimes
• Semiclassical Effects and the Onset of Inflation
• Naked Singularity Formation In f(R) Gravity
• First law of thermodynamics for dynamical apparent horizons and the entropy of Friedmann universes
• Gravitational collapse with tachyon field and barotropic fluid
• Event horizons and apparent horizons in spherically symmetric geometries
• Event horizons and apparent horizons in spherically symmetric geometries
• Trapped surfaces in spherical expanding open universes
• Entropy, energy and temperature-length inequality for Friedmann universes
• A Tolman-Bondi-Lemaitre Cell-Model for the Universe and Gravitational Collapse
• On the Definition of Averagely Trapped Surfaces
• Viaggiu entropy and the generalized second law in a flat FLRW Universe
• Trapped surfaces in cosmological spacetimes
• On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds
• The peculiar case of the Viaggiu holographic dark energy