  Observational identification of black holes as members of binary systems
requires the knowledge of the upper limit on the gravitational mass of a
neutron star. We use modern equations of state for neutron star matter, fitted
to experimental nucleon-nucleon scattering data and the properties of light
nuclei, to calculate, within the framework of Rhoades & Ruffini (1974), the
minimum upper limit on a neutron star mass. Regarding the equation of state as
valid up to twice nuclear matter saturation density, rho_{nm}, we obtain a
secure upper bound on the neutron star mass equal to 2.9 solar masses. We also
find that in order to reach the lowest possible upper bound of 2.2 solar
masses, we need understand the physical properties of neutron matter up to a
density of about 4 times rho_{nm}.
