  Supermassive black holes are now realized to exist in the centers of most
galaxies. The recent discoveries of luminous quasars at redshifts higher than 6
require that these black holes were assembled already when the Universe was
less than a billion years old. They might originate from the collapse of
supermassive stars, a scenario which could ensure a sufficiently rapid
formation. Supermassive stars are dominated by photon pressure and radiate at
their Eddington limit, which drives their quasi-static evolution to a final
relativistic instability. Above some critical value of the metallicity, their
collapse can lead to a gigantic explosion, powered by the energy release due to
hydrogen burning, but below this critical metallicity their collapse inevitably
ends in the formation of a black hole, accompanied by the emission of huge
amounts of energy in the form of neutrinos. Although collapsing supermassive
stars are the most powerful known burst sources of neutrinos, the associated
conditions do not appear favorable for producing highly relativistic outflows
that can explain cosmic gamma-ray bursts.
