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.

35 pages, 23 figures