Nonexistence of Baryon Number for Black Holes. II

Abstract

In a previous paper we showed that a static (nonrotating) black hole cannot be endowed with exterior scalar-meson or massive vector-meson fields. Here we show that the same is true for massive spin-2 meson fields. We also extend the above results to the case of a rotating stationary black hole. We conclude from our results that a black hole in its final (static or stationary) state cannot interact with the exterior world via the strong interactions which are mediated by meson fields such as the $\ensuremath{\pi}$ (scalar), $\ensuremath{\rho}$ (vector), and $f$ (spin-2). A direct consequence of this is the impossibility of determining the baryon number of the black hole by means of exterior measurements alone. This results in the transcendence of the law of baryon-number conservation as originally predicted by Wheeler. All the above conclusions hold both in general relativity and in the Brans-Dicke theory. We also show that the result of Hawking, that stationary black holes are identical in general relativity and in Brans-Dicke theory, holds even when the effects of the strong interactions (of the stellar material out of which the black hole was formed) are taken into account. Our final conclusion is that in both theories the Israel-Carter conjecture that "all stationary single-black-hole exteriors are of the Kerr-Newman type" holds even when the strong interactions are "turned on."