  Neutrinos are unique probes of core-collapse supernova dynamics, especially
in the case of black hole (BH) forming stellar collapses, where the
electromagnetic emission may be faint or absent. By investigating two 3D
hydrodynamical simulations of BH-forming stellar collapses of mass 40 and 75
M_sun, we identify the physical processes preceding BH formation through
neutrinos, and forecast the neutrino signal expected in the existing IceCube
and Super-Kamiokande detectors, as well as in the future generation DUNE
facility. Prior to the abrupt termination of the neutrino signal corresponding
to BH formation, both models develop episodes of strong and long-lasting
activity by the spiral standing accretion shock instability (SASI). We find
that the spiral SASI peak in the Fourier power spectrum of the neutrino event
rate will be distinguishable at 3 sigma above the detector noise for distances
up to O(30) kpc in the most optimistic scenario, with IceCube having the
highest sensitivity. Interestingly, given the long duration of the spiral SASI
episodes, the spectrograms of the expected neutrino event rate carry clear
signs of the evolution of the blue spiral SASI frequency as a function of time,
as the shock radius and post-shock fluid velocity evolve. Due to the high
accretion luminosity and its large-amplitude SASI-induced modulations, any
contribution from asymmetric (dipolar or quadrupolar) neutrino emission
associated with the lepton emission self-sustained asymmetry (LESA) is far
subdominant in the neutrino signal.
