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Is it possible for binary star systems to appear near a black hole?

Hardy Newman believes that binary star systems, or even triple star systems, appear only in the outer part of a spiral galaxy because these stars are far away from their central black hole, and therefore, contain less rich-neutron matter at their cores. So, the attraction force among them prevails against the repulsion force and if these stars are close enough to each other like those in binary star systems, they must revolve around each other to keep themselves from falling into each other.

Meanwhile, stars in the inner part of the spiral galaxy contain more rich-neutron matter than poor-neutron matter. So, repulsion force among them prevails against attraction force. It is impossible for them to revolve around each other because the interactive force among them are mostly repulsion force.

The answer to the question in the title is detailed in a video titled: "the general rule of matter distribution in the Universe", posted on the Youtube channel: Newman Online College and embedded in this page as follow:

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