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I understand that a solitary black hole has a spherical event horizon.

I was wondering whether this still stands in a binary system of two (let's say equal mass) black holes? Could the proximity of the two black holes (and the opposing gravitational pulls) mean that the event horizon of each black hole, that is facing in the direction of the other black hole, effectively appears to be flattened/distorted?

In other words, do the event horizons of a merging binary system come together like a Venn Diagram, or two soap bubbles?

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If two black holes are close to each other the shape of their horizons can be described by a function called the pair of pants (see Ref. 1, Ref. 2, Ref. 3, Ref. 4, Ref. 5):

pair of pants (x,y,t)

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