  We discuss three new equations of state (EOS) in core-collapse supernova
simulations. The new EOS are based on the nuclear statistical equilibrium model
of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects
and relativistic mean-field (RMF) interactions. We consider the RMF
parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our
spherically symmetric core-collapse supernova model, which is based on general
relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino
transport. The results obtained for the new EOS are compared with the widely
used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison
shows that the model description of inhomogeneous nuclear matter is as
important as the parameterization of the nuclear interactions for the supernova
dynamics and the neutrino signal. Furthermore, several new aspects of nuclear
physics are investigated: the HS EOS contains distributions of nuclei,
including nuclear shell effects. The appearance of light nuclei, e.g.,
deuterium and tritium is also explored, which can become as abundant as alphas
and free protons. In addition, we investigate the black hole formation in
failed core-collapse supernovae, which is mainly determined by the high-density
EOS. We find that temperature effects lead to a systematically faster collapse
for the non-relativistic LS EOS in comparison to the RMF EOS. We deduce a new
correlation for the time until black hole formation, which allows to determine
the maximum mass of proto-neutron stars, if the neutrino signal from such a
failed supernova would be measured in the future. This would give a constraint
for the nuclear EOS at finite entropy, complementary to observations of cold
neutron stars.
