J. R. OPPENHEIMER AND G. M. VOLKOFF
Department of Physics, University of California, Berkeley, California

It has been suggested that, when the pressure within stellar matter becomes high enough, a new phase consisting of neutrons will be formed. In this paper we study the gravitational equilibrium of masses of neutrons, using the equation of state for a cold Fermi gas, and general relativity. For masses under 1/3 solar masses only one equilibrium solution exists, which is approximately described by the nonrelativistic Fermi equation of state and Newtonian gravitational theory. For masses 1/3 < M < 3/4 solar masses two solutions exist, one stable and quasi-Newtonian, one more condensed, and unstable. For masses greater than 3/4 solar masses there are no static equilibrium solutions. [The maximum mass of a stable neutron star is now believed to be about 3 solar masses, not 3/4 solar masses. Since Oppenheimer did his calculations, physicists learned that the repulsive force between closely packed neutrons is greater than he thought.] These results are qualitatively confirmed by comparison with suitably chosen special cases of the analytic solutions recently discovered by Tolman. A discussion of the probable effect of deviations from the Fermi equation of state suggests that actual stellar matter after the exhaustion of thermonuclear sources of energy will, if massive enough, contract indefinitely, although more and more slowly, never reaching true equilibrium.