Can there be such a thing as a black hole cluster, with multiple black holes in very small distances?
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It is probably impossible for there to be a black hole cluster, since the relative gravity of all the black holes would cause them all to collapse in on each other and form a larger black hole. Star clusters exist because the relative gravity of each star helps them orbit around inside the cluster; still, exploding supernovas and colliding stars cause dramatic changes inside the cluster (it should be pointed out that this happens on a monumentally enormous scale, measured in parsecs, each about 3.26 lightyears). Because of their much higher gravity, however, black holes in a cluster would probably be buffeted by their respective gravities much more and so would collide more frequently. It is possible for two black holes to be locked in orbit with each other, each bleeding off the energy and matter surrounding the other, until they eventually collide and merge.
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