Nonexistence of Baryon Number for Static Black Holes

Wheeler has conjectured that black holes should have no well-defined baryon number, and that as a result the law of conservation of baryons should be transcended in black-hole physics. We show here that a static black hole cannot have any exterior classical scalar or massive vector fields. We consider the modifications that would arise from a quantum-theoretical treatment, and we conclude that such a black hole cannot interact with the exterior world via virtual mesons such as the π and ρ. Because of this we find no way for external measurements to assign unambiguously a baryon number to such a black hole in agreement with Wheeler's prediction.