The last stage
What remains of the supernova explosion are the debris of the explosions, which will be seen for thousands of years, and the core of the exploded star; this core becomes a neutron star, if the core mass is between 1.4 and about 2.5 solar masses, or a black hole, if the core is more massive than 2.5 ~3 solar masses. In the former case, if the neutron star is spinning, we have pulsars. In the latter case, gravity is so strong that it wins out over the interactions between neutrons and there is no limit at how dense collapsing matter can become.
Vela supernova Remnant in X-ray. credits: ROSAT MPE NASA
At that point density is so high that not even light (electromagnetic radiation) can escape from a black hole. A black hole has an event horizon, or a radius, called Schwarzschild radius; no particle or radiation within this radius can escape the pull of the black hole. The radius is proportional to the matter in the black hole (a black hole would have a radius of 3 Km if its mass were 1 solar mass). It is important to note that this radius is an information barrier; thus we don't know what is "inside" a black hole, since no information can come to us from the inside. Einstein's theory of general relativity predicts that matter becomes infinitely dense at the center of the black hole. This point is called a singularity. It is possible that Einstein's theory breaks down at that distance, and thus we might not have yet a good description of the inside of the black hole.
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