We investigate the explosion of stars with zero-age main-sequence masses between 20 and 35 solar masses and varying degrees of rotation and magnetic fields including ones commonly considered progenitors of gamma-ray bursts (GRBs). The simulations, combining special relativistic magnetohydrodynamics, a general relativistic approximate gravitational potential, and two-moment neutrino transport, demonstrate the viability of different scenarios for the post-bounce evolution. Having formed a highly massive proto-neutron star (PNS), several models launch successful explosions, either by the standard supernova mechanism based on neutrino heating and hydrodynamic instabilities or by magnetorotational processes. It is, however, quite common for the PNS to collapse to a black hole (BH) within a few seconds. Others might produce proto-magnetar-driven explosions. We explore several ways to describe the different explosion mechanisms. The competition between the timescales for advection of gas through the gain layer and heating by neutrinos provides an approximate explanation for models with insignificant magnetic fields. The fidelity of this explosion criterion in the case of rapid rotation can be improved by accounting for the strong deviations from spherical symmetry and mixing between pole and equator. We furthermore study an alternative description including the ram pressure of the gas falling through the shock. Magnetically driven explosions tend to arise from a strongly magnetised region around the polar axis. In these cases, the onset of the explosion corresponds to the equality between the advection timescale and the timescale for the propagation of Alfven waves through the gain layer.
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