[pzhon]

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Binary stars orbit each other around a common center of mass. Is it possible that the combined mass of a binary star system be such that an event horizon is created?

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A useful consideration is the event horizon radius. For a non-rotating, uncharged black hole, this is linear in the mass, m * 2G/c^2 IIRC. That means if the rotation is not significant, and you can contain the two pieces in disjoint spheres, then for the sum to be a black hole, one of the pieces must be a black hole.

Some rotation is involved. The event horizon of a rotating black hole is smaller than the event horizon of a nonrotating black hole. I don't know whether that allows two pieces to avoid being black holes due to rotation (in opposite directions) while the union is a black hole.