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There are well-known Penrose diagrams for black holes:

And for collapsing star:

Diagram for collapsing star is obtained by joining two Penrose diagrams:

Is it possible to join diagrams for two black holes?

These black holes will rotate and emit gravitational waves and after will collapse to one BH. How to join diagrams in such situation?

Maybe one can construct diagram witch approximately describe such process?

Qmechanic
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Nikita
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    Afaik Penrose diagrams only work for spherically symmetric spacetimes – Prof. Legolasov Nov 09 '20 at 22:19
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    @Prof.Legoslav What does "work" in you comment mean? I would think you can draw the diagram for any 2D timelike submanifold – Umaxo Nov 10 '20 at 10:14
  • +1 for the star not collapsing to a point like in incorrect diagrams by Ben Crowell (user4552) here: https://physics.stackexchange.com/questions/5031/can-black-holes-form-in-a-finite-amount-of-time/424256 – safesphere Nov 10 '20 at 22:52

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No, it isn't possible to make a Penrose diagram for two black holes. In a Penrose diagram, we take advantage of symmetries to reduce the number of spacetime dimensions from 4 to 2. A spacetime containing two black holes doesn't have enough symmetry to allow that.

user279372
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  • But finally we will have symmetric space time. Initial space time is not symmetric, but maybe this symmetry can be considered as approximate? – Nikita Nov 09 '20 at 23:48