No-hair theorem

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The no-hair theorem (which is a hypothesis) states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, angular momentum, and electric charge.^[1] Other characteristics (such as geometry and magnetic moment) are uniquely determined by these three parameters, and all other information (for which "hair" is a metaphor) about the matter that formed a black hole or is falling into it "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole "settles down" (by emitting gravitational and electromagnetic waves). Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair",^[1] which was the origin of the name.

In a later interview, Wheeler said that Jacob Bekenstein coined this phrase.^[2]

Richard Feynman objected to the phrase that seemed to me to best symbolize the finding of one of the graduate students: graduate student Jacob Bekenstein had shown that a black hole reveals nothing outside it of what went in, in the way of spinning electric particles. It might show electric charge, yes; mass, yes; but no other features – or as he put it, "A black hole has no hair". Richard Feynman thought that was an obscene phrase and he didn't want to use it. But that is a phrase now often used to state this feature of black holes, that they don't indicate any other properties other than a charge and angular momentum and mass.^[3]

The first version of the no-hair theorem for the simplified case of the uniqueness of the Schwarzschild metric was shown by Werner Israel in 1967.^[4] The result was quickly generalized to the cases of charged or spinning black holes.^[5][6] There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved by results of Stephen Hawking, Brandon Carter, and David C. Robinson, under the additional hypothesis of non-degenerate event horizons and the technical, restrictive and difficult-to-justify assumption of real analyticity of the space-time continuum.