Black Hole Hair: Twenty{{ve Years After

Originally regarded as forbidden, black hole \hair" are elds associated with a stationary black hole apart from the gravitational and electromagnetic ones. Several stable stationary black hole solutions with gauge or Skyrme eld hair are known today within general relativity. We formulate here a \no scalar{ hair" conjecture, and adduce some new theorems that almost establish it by ruling out-for all but a small parameter range-scalar eld hair of spherical black holes in general relativity, whether the eld be self{interacting, coupled to an Abelian gauge eld, or nonminimally coupled to gravity. Twenty{{ve years ago Wheeler enunciated the Israel{Carter conjecture, today colloquially known as \black holes have no hair" 1]. Inmensely innuential in black hole physics, this conjecture has long been regarded as a theorem by large sectors of the gravity{particle physics community. On the other hand, the proliferation in the 1990's of solutions for stationary black holes equipped with various exterior elds 2] has led many modern workers to regard the conjecture as having fallen by the wayside. As I hope to make clear here, both these extreme views are oo the mark. How did this complicated situation emerge ? By 1965 the charged Kerr{ Newman black hole metric was known. Inspired by Israel's uniqueness theorems for the Schwarzschild and Reissner{Nordstrr om (RN) black holes 3] and Carter and Wald's uniqueness theorems for the Kerr black hole 4], Wheeler anticipated that \collapse leads to a black hole endowed with mass and charge and angular momentum, but, so far as we can now judge, no other free parameters". Wheeler stressed that quantum numbers such as baryon number or strangeness can have no place in the external description of a black hole. Wheeler focused on mass, electric charge and angular momentum because they are all conserved quantities subject to a Gauss law. One can thus determine these properties of a black hole by measurements from afar. Obviously this reasoning has to be completed by including magnetic charge as a fourth parameter ; magnetic charge is conserved in Einstein{Maxwell theory, posesses a Gauss law,