Why do you think we find black holes at the center of galaxies and not on the arms?

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Black holes are celestial objects that are characterized by extremely high density (mass per unit volume) and exceptionally high gravitational pull. The gravitational pull of a black hole is so strong that not even light can escape it and hence the name 'black hole'. A black hole is the final life stage of a massive star. To put things in perspective, our own Sun may end up as a black hole of less than 6 km diameter. All the mass of Sun would still be there, giving it immense density and the gravitational pull would remain the same. 

The exceptionally high gravity of a black hole allows it to pull other objects towards it and hence would lie in a region of a lot of matter and gases. The centers of galaxies are ideal for that purpose, since they will contain much more matter than their peripheries. If a massive or super black hole is at the arms of a galaxy, it would start pulling everything towards it, which may cause a number of stars and other celestial bodies to rotate around it (and ultimately fall into it) and the arm would no longer remain the same. This may cause the shape of the galaxy to be distorted and a new center may form around this super black hole. Thus, black holes are ideally situated at or around the center of the galaxies.

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