With the first generation of ground-based gravitational wave laser interferometers (LIGO, VIRGO, GEO600, TAMA) just becoming operational, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable
gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (for simplified EOS and neglecting neutrino transport and magnetic fields), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of the 3+1 Einstein equations. Telling from this recent work, the prospects of detection of (burst) gravitational radiation from stellar core collapse seems only likely in the case of Galactic events, but only marginal for sources located as far as the Virgo cluster, i.e. at distances with an increased supernova event rate. In this talk, the current status of relativistic core collapse simulations will be discussed, with the emphasis given on the modelling of the collapse dynamics and on the computation of the gravitational radiation in those numerical approaches.
Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein equations will be reported, as well as extensions of this approximation (which we call CFC+) and investigations within the framework of characteristic numerical relativity (with no approximation for the spacetime dynamics). In the former two approaches results for both, gravitational collapse leading to black hole formation and magnetized core collapse in the "test magnetic field" approximation, will be briefly discussed as well.
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