Recent mathematical results in gravitational collapse

Astronomy and Astrophysics – Astronomy

Scientific paper

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Black Holes (Astronomy), Einstein Equations, Gravitational Collapse, Boundary Conditions, Wave Equations

Scientific paper

The Einstein equations where the energy tensor is that of a scalar field are discussed for the spherically symmetric case. Previous work, confined to the domain of outer communications, found that when the final Bondi mass M1 is greater than zero, as the retarded time measured by faraway observers tends to infinity, a black hole of mass M1 forms surrounded by vacuum. If the initial future cone has an annular region such that the mass contained in the region bears to the largest radius a ratio that is large compared to the ratio of the radii minus 1, then a trapped sphere forms in the future the mass of which is bounded from below by a positive number depending only on the two initial radii. Thus M1 has a positive lower bound. This paper goes beyond the event horizon to study the structure of the apparent horizon and the singular boundary, obtaining a lower bound for the rate of blowup of the curvature at this boundary.

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