  We investigate the structure of neutron stars shortly after they are born,
when the entropy per baryon is of order 1 or 2 and neutrinos are trapped on
dynamical timescales. In all cases, the thermal effects for an entropy per
baryon of order 2 or less are small when considering the maximum neutron star
mass. Neutrino trapping, however, significantly changes the maximum mass due to
the abundance of electrons. When matter is allowed to contain only nucleons and
leptons, trapping decreases the maximum mass by an amount comparable to, but
somewhat larger than, the increase due to finite entropy. When matter is
allowed to contain strongly interacting negatively charged particles, in the
form of strange baryons, a kaon condensate, or quarks, trapping instead results
in an increase in the maximum mass of order $0.2M_\odot$, which adds to the
effects of finite entropy. The presence of negatively-charged particles has two
major implications. First, the value of the maximum mass will decrease during
the early evolution of a neutron star as it loses trapped neutrinos, so that if
a black hole forms, it either does so immediately after the bounce or it is
delayed for a neutrino diffusion timescale of $\sim 10$ s. The latter case is
most likely if the maximum mass of the hot star with trapped neutrinos is near
$1.5M_\odot$. In the absence of negatively-charged hadrons, black hole
formation would be due to accretion and therefore is likely to occur only
immediately after bounce. Second, the appearance of hadronic negative charges
results in a general softening of the equation of state that may be observable
in the neutrino luminosities and average energies. Further, these additional
negative charges decrease the electron fraction and may be observed in the
relative excess of electron neutrinos compared to other neutrinos.
