  We present results of three-dimensional (3D), radiation-magnetohydrodynamics
(MHD) simulations of core-collapse supernovae in full general relativity (GR)
with spectral neutrino transport. In order to study the effects of progenitor's
rotation and magnetic fields, we compute three models, where the precollapse
rotation rate and magnetic fields are included parametrically to a 20
M$_{\odot}$ star. While we find no shock revival in our two non-magnetized
models during our simulation times ($\sim500$ ms after bounce), the
magnetorotationally (MR) driven shock expansion immediately initiates after
bounce in our rapidly rotating and strongly magnetized model. We show that the
expansion of the MR-driven flows toward the polar directions is predominantly
driven by the magnetic pressure, whereas the shock expansion toward the
equatorial direction is supported by neutrino heating. Our detailed analysis
indicates that the growth of the so-called kink instability may hinder the
collimation of jets, resulting in the formation of broader outflows.
Furthermore we find a dipole emission of lepton number, only in the MR
explosion model, whose asymmetry is consistent with the explosion morphology.
Although it is similar to the lepton-number emission self-sustained asymmetry
(LESA), our analysis shows that the dipole emission occurs not from the
protoneutron star convection zone but from above the neutrino sphere indicating
that it is not associated with the LESA. We also report several unique neutrino
signatures, which are significantly dependent on both the time and the viewing
angle, if observed, possibly providing a rich information regarding the onset
of the MR-driven explosion.
