Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse

Charles W. Misner and David H. Sharp
Phys. Rev. 136, B571 – Published 26 October 1964
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Abstract

The Einstein equations for a spherically symmetrical distribution of matter are studied. The matter is described by the stress-energy tensor of an ideal fluid (heat flow and radiation are therefore excluded). In this case, the Einstein equations give a generalization of the Oppenheimer-Volkoff equations of hydrostatic equilibrium so as to include an acceleration term and a contribution to the effective mass of a shell of matter arising from its kinetic energy. A second equation also appears in this time-dependent case; it gives the rate of change of an appropriate "total energy" m(r, t) of each fluid sphere in terms of the work done on this sphere by the fluid surrounding it. These equations would be an appropriate starting point for a study of relativistic gravitational collapse in which an adiabatic equation of state more realistic than the p=0 form of Oppenheimer and Snyder could be used.

  • Received 15 June 1964

DOI:https://doi.org/10.1103/PhysRev.136.B571

©1964 American Physical Society

Authors & Affiliations

Charles W. Misner

  • Department of Physics and Astronomy, University of Maryland, College Park, Maryland

David H. Sharp*

  • Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

  • *NSF Postdoctoral Fellow, 1963-64.

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Issue

Vol. 136, Iss. 2B — October 1964

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