Authors

Beckedorff, David L.
Misner, Charles W.

Title

Terminal Configurations of Stellar Evolution

Date of Issue

1962

Publisher

Princeton University, Department of Mathematics

Citation

Beckedorff 1962

Series/Report No.

None

Identifiers

 

Type

Article

Language

English (United States)

 

Subject Keywords

continued gravitational contraction
Oppenheimer-Snyder
gravitational collapse
black holes
Schwarzschild metric
Friedmann cosmology
Finkenstein coordinates
Kruskal coordinates
general relativity
Einstein equations

Abstract

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.

Sponsors

Princeton University--Department of Mathematics, U. S. Office of Naval Research

Description

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.

 

File

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