I just heard Carlo Rovelli explain a scenario for blackholes, let's see if I can reproduce it.
Take a supermassive star. As it reaches the point where it has fused together the last fusionable elements, it begins to cool. Since the heat generated by nuclear fusion has been the only thing preventing gravity from collapsing all the matter into the centre, it begins to collapse. Matter from the star rushes towards the centre very fast, causing an implosion. This throws most of the matter back out into space, but at the very core matter becomes super-compressed. All the protons and electrons are converted into neutrons and these are squeezed into very dense neutronium that takes up very little space.
Relativity says that above a certain mass the neutron core of the star continues to be compressed by gravity and that there is no limit to this compression. If there is enough matter to start with, the neutronium becomes so dense that nothing can reach escape velocity and it becomes a blackhole. Compression continues forever making the star effectively infinitely small with infinite density.
However, regions of infinite density are ruled out by quantum mechanics. Even a blackhole must have a finite density - the smallest possible scale is the Planck length of 10-33m, and the smallest possible volume is a Planck cubed. Rovelli suggests that a blackhole collapses down to a minimum, but finite, volume and then explodes outwards again. And this process takes about 1 millisecond.
What? If we go back to Relativity it says that the closer we are to a large mass, the slower time will go for us compared to a distance observer. This is because of the fixed speed of light. Near a large mass, space is tightly curved and distances between points are compressed, but light goes the same speed (300,000 ms-1), so in order for the speed (ms-1) to remain the same, time must slow down. If a blackhole caused infinite density, then time would have to cease. But since matter it cannot be infinitely dense, due to the limit on how small a volume of space is, time must continue to pass, however slowly. But since the time dilation occurs to everything at once, subjectively time would probably continue to pass at the same rate near the mass. It is only a distant observer who would see things slowing down.
If we were able to travel down into the heart of a blackhole as it collapsed and bounced back, it would seem to take about 1 ms to us. Subjectively, inside the blackhole time would continue pass at normal speed. But if we are looking at a blackhole collapsing from several light years away, the process would appear to take billions of years. And this is why we don't see blackholes exploding.
If blackholes do explode then we ought to be able to see it, and this is something that astronomers can look for. Perhaps such explosions would be visible to the LIGO gravity wave detector or some future detector which is more sensitive?
At the moment this is just hand-wavy stuff. Something other than a singularity must exist in a blackhole, because of quantum mechanics, but we're not sure what it is yet. This is quite a cool scenario though.