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" 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 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