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In general relativity exist very famous no-hair theorem:

The no-hair theorem states that all black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.

But I never face with generalisations of such theorem for several black holes and also for theories with non-Abelian fields and couple of scalars.

Did somebody obtain some results in generalisations of no-hair theorem in thus direction?

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  • $\begingroup$ I've once stumbled upon a no hair theorem for proca fields: arxiv.org/abs/gr-qc/0210001 $\endgroup$
    – Noone
    Commented Nov 8, 2020 at 17:34
  • $\begingroup$ Also i do not understand what you mean by several black holes. $\endgroup$
    – Noone
    Commented Nov 8, 2020 at 17:35
  • $\begingroup$ @ApolloRa , How to extend no-hair theorem for 2 black holes? Foe 3 black holes? $\endgroup$
    – Nikita
    Commented Nov 8, 2020 at 17:42

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There is a Living Reviews in Relativity article on the status of stationary black hole solutions. The upshot is that for non abelian gauge theories (and some other nonlinear theories) you can find “hairy” solutions that are not simply characterized by their charges.

For multiple black holes, I’m not even sure how to phrase the question as it should be near impossible to form a stationary solution with a finite number of black holes. (Unless they have extremal charge.)

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