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
OppenheimerSnyder
gravitational collapse
black holes
Schwarzschild metric
Friedmann cosmology
Finkenstein coordinates
Kruskal coordinates
general relativity
Einstein equations

Abstract

The
OppenheimerSnyder
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 zeropressure 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 3surface 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 UniversityDepartment 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.





