  We present a new multi-dimensional radiation-hydrodynamics code for massive
stellar core-collapse in full general relativity (GR). Employing an M1
analytical closure scheme, we solve spectral neutrino transport of the
radiation energy and momentum based on a truncated moment formalism. Regarding
neutrino opacities, we take into account a baseline set in state-of-the-art
simulations, in which inelastic neutrinoelectron scattering, thermal neutrino
production via pair annihilation and nucleonnucleon bremsstrahlung are
included. While the Einstein field equations and the spatial advection terms in
the radiation-hydrodynamics equations are evolved explicitly, the source terms
due to neutrino-matter interactions and energy shift in the radiation moment
equations are integrated implicitly by an iteration method. To verify our code,
we first perform a series of standard radiation tests with analytical solutions
that include the check of gravitational redshift and Doppler shift. A good
agreement in these tests supports the reliability of the GR multi-energy
neutrino transport scheme. We then conduct several test simulations of
core-collapse, bounce, and shock-stall of a 15Msun star in the Cartesian
coordinates and make a detailed comparison with published results. Our code
performs quite well to reproduce the results of full-Boltzmann neutrino
transport especially before bounce. In the postbounce phase, our code basically
performs well, however, there are several differences that are most likely to
come from the insufficient spatial resolution in our current 3D-GR models. For
clarifying the resolution dependence and extending the code comparison in the
late postbounce phase, we discuss that next-generation Exaflops-class
supercomputers are at least needed.
