Infinite Red-Shifts in General Relativity

Thumbnail Image


Publication or External Link





T. Gold, "The Nature of Time", Chapter 6



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. 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 first written presentation were carried out by Beckedorff and provided his Princeton senior thesis in April 1962. ( ) In this 1963 presentation Misner emphasizes that the properties of matter at high densities are irrelevant to the question of whether such a collapse can occur for sufficiently massive objects. The detailed computations by Beckedorff are here linked in an appended file.


This Cornell 1967 publication is a taped transcript of a talk given in June 1963. It presented a soon-to-be-standard insight into idealized spherical gravitational collapse, and may have influenced significant participants at that meeting such as Wheeler, Penrose, and Sciama. 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