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We show that the existence of black holes with classical skyrmion hairinvalidates standard proofs that global charges, such as the baryon number,cannot be conserved by a black hole. By carefully analyzing the standardarguments based on a Gedankenexperiment in which a black hole isseemingly-unable to return the baryon number that it swallowed, we identifyinconsistencies in this reasoning, which does not take into the account neitherthe existence of skyrmion black holes nor the baryon/skyrmion correspondence.We then perform a refined Gedankenexperiment by incorporating the new knowledgeand show that no contradiction with conservation of baryon number takes placeat any stage of black hole evolution. Our analysis also indicates no conflictbetween semi-classical black holes and the existence of baryonic gaugeinteraction arbitrarily-weaker than gravity. Next, we study classical crosssections of a minimally-coupled massless probe scalar field scattered by askyrmion black hole. We investigate how the skyrmion hair manifests itself bycomparing this cross section with the analogous cross section caused by aSchwarzschild black hole which has the same ADM mass as the skyrmion blackhole. Here we find an order-one difference in the positions of thecharacteristic peaks in the cross sections. The peaks are shifted to smallerscattering angles when the skyrmion hair is present. This comes from the factthat the skyrmion hair changes the near horizon geometry of the black hole whencompared to a Schwarzschild black hole with same ADM mass. We keep the study ofthis second aspect general so that the qualitative results which we obtain canalso be applied to black holes with classical hair of different kind.

Skyrmion Black Hole Hair: Conservation of Baryon Number by Black Holes and Observable Manifestations