We investigate the structure of neutron stars shortly after they are b
orn, when the entropy per baryon is of order 1 or 2 and neutrinos are
trapped on dynamical timescales. We find that the structure depends mo
re sensitively on the composition of the star than on its entropy, and
that the number of trapped neutrinos play an important role in determ
ining the composition. Since the structure is chiefly determined by th
e pressure of the strongly interacting constituents and the nature of
the strong interactions is poorly understood at high density, we consi
der several models of dense matter, including matter with strangeness-
rich hyperons, a kaon condensate and quark matter. In all cases, the t
hermal effects for an entropy per baryon of order 2 or less are small
when considering the maximum neutron star mass. Neutrino trapping, how
ever, significantly changes the maximum mass due to the abundance of e
lectrons. When matter is allowed to contain only nucleons and leptons,
trapping decreases the maximum mass by an amount comparable to, but s
omewhat larger than, the increase due to finite entropy. When matter i
s allowed to contain strongly interacting negatively charged particles
, in the form of strange baryons, a kaon condensate, or quarks, trappi
ng instead results in an increase in the maximum mass, which adds to t
he effects of finite entropy. A net increase of order 0.2M. occurs. Th
e presence of negatively-charged particles has two major implications
for the neutrino signature of gravitational collapse supernovae. First
, the value of the maximum mass will decrease during the early evoluti
on of a neutron star as it loses trapped neutrinos, so that if a black
hole forms, it either does so immediately after the bounce (accretion
being completed in a second or two) or it is delayed for a neutrino d
iffusion timescale of similar to 10 s. The latter case is most likely
if the maximum mass of the hot star with trapped neutrinos is near 1.5
M.. In the absence of negatively-charged hadrons, black hole formation
would be due to accretion and therefore is likely to occur only immed
iately after bounce. Second, the appearance of hadronic negative charg
es 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.