Relativistic Equations for Spherical Gravitational Collapse with Escaping Neutrinos

The general-relativity equations for the dynamics of a self-gravitating sphere of ideal fluid as given by Misner and Sharp are modified to allow an extremely simplified heat-transfer process in which internal energy is converted (at some rate controlled by an equation of state) into an outward flux of neutrinos which have no subsequent interaction with matter. This outward flux of radiation carries with it an inward non-Newtonian gravitational force field. Thus, if a portion $\Delta m$ of some central mass is converted into escaping radiation, the corresponding energy increase $\sim \frac{G\Delta m}{R}$ of each unit mass of surrounding matter is seen to be the work done by this non-Newtonian inward impulse accompanying the radiation.