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

TL;DR

This paper demonstrates that black holes with skyrmion hair can conserve baryon number, challenging previous no-hair theorems, and shows how skyrmion hair affects observable scattering cross sections compared to standard black holes.

Contribution

It reveals that classical skyrmion hair allows baryon number conservation in black holes and identifies observable differences in scattering signatures due to skyrmion hair.

Findings

Skyrmion black holes do not violate baryon number conservation.

Skyrmion hair shifts scattering peaks to smaller angles.

Differences in near horizon geometry affect scattering cross sections.

Abstract

We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence. We then perform a refined Gedankenexperiment by incorporating the new knowledge and show that no contradiction with conservation of baryon number takes place at any stage of black hole evolution. Our analysis also indicates no conflict between semi-classical black holes and the existence of baryonic gauge interaction arbitrarily-weaker than gravity. Next, we study classical cross sections of a minimally-coupled massless probe scalar field scattered by a skyrmion black hole. We investigate how the skyrmion hair manifests itself by comparing this cross section with the analogous cross section caused by a Schwarzschild black hole which has the same ADM mass as the skyrmion black hole. Here we find an order-one difference in the positions of the characteristic peaks in the cross sections. The peaks are shifted to smaller scattering angles when the skyrmion hair is present. This comes from the fact that the skyrmion hair changes the near horizon geometry of the black hole when compared to a Schwarzschild black hole with same ADM mass. We keep the study of this second aspect general so that the qualitative results which we obtain can also be applied to black holes with classical hair of different kind.