  We apply our recently developed code for spherically symmetric, fully general
relativistic (GR) Lagrangian hydrodynamics and multigroup flux-limited
diffusion neutrino transport to examine the effects of GR on the hydrodynamics
and transport during collapse, bounce, and the critical shock reheating phase
of core collapse supernovae. Comparisons of models computed with GR versus
Newtonian hydrodynamics show that collapse to bounce takes slightly less time
in the GR limit, and that the shock propagates slightly farther out in radius
before receding. After a secondary quasistatic rise in the shock radius, the
shock radius declines considerably more rapidly in the GR simulations than in
the corresponding Newtonian simulations. During the shock reheating phase, core
collapse computed with GR hydrodynamics results in a substantially more compact
structure from the center out to the stagnated shock. The inflow speed of
material behind the shock is also increased. Comparisons also show that the
luminosity and rms energy of any neutrino flavor during the shock reheating
phase increases when switching from Newtonian to GR hydrodynamics, and
decreases when switching from Newtonian to GR transport. This latter decrease
in neutrino luminosities and rms energies is less in magnitude than the
increase that arise when switching from Newtonian to GR hydrodynamics, with the
result that a fully GR simulation gives higher neutrino luminosities and harder
neutrino spectra than a fully Newtonian simulation of the same precollapse
model.
