  We present results from the first generation of multi-dimensional general
relativistic neutrino hydrodynamics simulations of core-collapse supernovae. A
comparison with models computed using either the purely Newtonian approximation
or the "effective gravitational potential" approach reveals appreciable
quantitative differences in the heating conditions and the gravitational wave
spectra. Our results underscore the important role of general relativity in the
supernova problem (which appears to be on par with other important factors such
as the dimensionality and the equation of state) both for our understanding of
the explosion dynamics as well as for predictions of observable signatures.
