  We present results from general-relativistic (GR) three-dimensional (3D)
core-collapse simulations with approximate neutrino transport for three
non-rotating progenitors (11.2, 15, and 40 Msun) using different nuclear
equations of state (EOSs). We find that the combination of progenitor's higher
compactness at bounce and the use of softer EOS leads to stronger activity of
the standing accretion shock instability (SASI). We confirm previous
predications that the SASI produces characteristic time modulations both in
neutrino and gravitational-wave (GW) signals. By performing a correlation
analysis of the SASI-modulated neutrino and GW signals, we find that the
correlation becomes highest when we take into account the time-delay effect due
to the advection of material from the neutrino sphere to the proto-neutron star
core surface. Our results suggest that the correlation of the neutrino and GW
signals, if detected, would provide a new signature of the vigorous SASI
activity in the supernova core, which can be hardly seen if neutrino-convection
dominates over the SASI.
