What is the relationship between a quasar, black hole, and a singularity?
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When stars 20 to 25 times size of Sun end their lives in a supernova explosion, their cores collapse and gravity wins out over all other forces that may hold the star.
Eventually, the star collapses so much that it is contained within a small boundary from which even light cannot escape. At this point, the black hole is extremely tiny e.g. a black hole with the mass of the Sun would fit in a size as small as a town.
Singularity is referred to a quantity, which approaches infinity as another parameter goes to zero. An example is a black hole, in which a very large mass gets concentrated in so short a distance that gravitational forces become infinite and all matter and energy (including light or electromagnetic energy) cannot escape it. At this level all physical laws break down.
A quasar is a point-like source that is associated with radiatively efficient emission of an active galaxy, which means that its central black hole and is undergoing high rates of mass accretion. They are typically among the most distant objects we can observe and have highest red shifts and thus on the fringes of universe.
However, they emit huge amount of light and many of them are bright in radio spectrum too. They were found to be quite small by Astrophysical standards - just the size of our solar system and only way to generate such huge amounts of energy is from matter falling towards a Black Hole. As such it is believed that Quasars are massive black holes in the center of young galaxies.