black hole - Why do certain massive stars leave no remnants?

The gap appears because of pair instability supernovae. In short, as one looks at such massive stellar cores at increasing temperatures, an ever-larger fraction of the photons are sufficiently energetic to spontaneously form electron-positron pairs. True, they soon recombine, but there is nevertheless a loss in (radiation) pressure, which causes contraction, and thus a further increase of temperature. If unstable, as appears to be the case in such massive stars, this leads to more high-energy photons, more pairs, and a further loss of pressure.

Models of such objects suggest that the collapse leads to a sudden, rapid ignition of oxygen- and silicon-burning reactions. In a mass range between about 150 and 250 solar masses (corresponding to core masses of very roughly half of that), the thermonuclear explosion is enough to rip the core apart, and there's nothing left to collapse. This is a bit like how the sudden onset of carbon burning destroys white dwarfs in type Ia supernovae. More massive cores are more strongly bound by gravity, and models suggest that the nuclear explosion isn't enough to unbind the core.

So below about 150 solar masses (and at higher metallicities, I think), the core doesn't reach pair-unstable conditions. Above about 250 solar masses, the induced nuclear explosion isn't powerful enough to destroy the core.