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Authors
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Beckedorff, David L.
Misner, Charles W.
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Title
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Terminal
Configurations of Stellar Evolution
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Date of Issue
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1962
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Publisher
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Princeton University, Department of
Mathematics
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Citation
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Beckedorff 1962
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Series/Report
No.
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None
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Identifiers
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Type
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Article
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Language
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English
(United States)
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Subject
Keywords
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continued
gravitational contraction
Oppenheimer-Snyder
gravitational collapse
black holes
Schwarzschild metric
Friedmann cosmology
Finkenstein coordinates
Kruskal coordinates
general relativity
Einstein equations
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Abstract
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The
Oppenheimer-Snyder
description of continued gravitational collapse is reformulated as a
matching together of two familiar solutions of the Einstein
gravitational equations. From one solution, the Friedmann
cosmology with zero-pressure matter, one selects the interior of a
sphere whose points move on timelike
geodesics. From the other solution one selects the exterior of such a
sphere in the vacuum Schwarzschild solution. It is shown that for the
expected choice of parameters (sphere circumference, interior density,
exterior mass) these can be fit together smoothly enough to satisfy the
Einstein equations. The matching conditions are that the first and
second fundamental forms at the joining 3-surface agree. The
description of this collapsing ball of matter survives its passage
through Finkelstein’s
(1958) smooth “unidirectional membrane” at r=2M and is most
conveniently presented using the Kruskal
coordinates for the Schwarzschild solution. This project was proposed
and designed by Misner (choice of solutions and matching requirements),
but the execution and presentation were carried out by Beckedorff and provided his Princeton
senior thesis in April 1962.
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Sponsors
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Princeton University--Department of Mathematics, U. S.
Office of Naval Research
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Description
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For
comments on the impact of this work see: K. S. Thorne "Black Holes
..." (Norton 1994) p.246; J. A. Wheeler and K. Ford "Geons, Black Holes, ..." (Norton 1998) p.295;
M. Bartusiak "Einstein's Unfinished Sumphony" (Joseph Henry Press 2000) p.61.
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