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A neutron star that is left-over after a supernova is actually a remnant of the massive star which went supernova. Black Hole formation during the collapse of massive stars which precedes a supernova can proceed in a couple of different ways.
Pulsars are rotating neutron stars observed to have pulses of radiation at very regular intervals that typically range from milliseconds to seconds. Pulsars have very strong magnetic fields which funnel jets of particles out along the two magnetic poles.
Step-by-step explanation: