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

Gia Dvali, Alexander Gußmann

TL;DR

The paper argues that black holes with classical skyrmion hair provide a consistent framework in which baryon number can be conserved during black hole evolution, challenging standard folk-theorem proofs that global charges cannot survive evaporation. It refines the traditional thought experiments by incorporating the skyrmion/baryon correspondence and derives regimes and scales, notably the skyrmion length $L$ and the horizon scale $r_h$, where hair re-emerges and baryon charge is visible. It further demonstrates observable consequences of skyrmion hair via classical scattering of a massless scalar, revealing order-one shifts in glory peak positions due to changes in near-horizon geometry, and discusses broader implications for the weak gravity conjecture and the viability of global or weakly gauged symmetries. Overall, the work links topological baryon number with classical hair, providing testable predictions and suggesting that semi-classical BH physics does not require baryon-number violation in the presence of skyrmion hair.

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.

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

TL;DR

The paper argues that black holes with classical skyrmion hair provide a consistent framework in which baryon number can be conserved during black hole evolution, challenging standard folk-theorem proofs that global charges cannot survive evaporation. It refines the traditional thought experiments by incorporating the skyrmion/baryon correspondence and derives regimes and scales, notably the skyrmion length and the horizon scale , where hair re-emerges and baryon charge is visible. It further demonstrates observable consequences of skyrmion hair via classical scattering of a massless scalar, revealing order-one shifts in glory peak positions due to changes in near-horizon geometry, and discusses broader implications for the weak gravity conjecture and the viability of global or weakly gauged symmetries. Overall, the work links topological baryon number with classical hair, providing testable predictions and suggesting that semi-classical BH physics does not require baryon-number violation in the presence of skyrmion hair.

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.

Paper Structure

This paper contains 22 sections, 61 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Skyrmion black holes
  3. The skyrme Lagrangian
  4. The appearance of solitonic configurations (skyrmions)
  5. Gravitating skyrmions and skyrmions as black hole hair
  6. Skyrmion black holes as baryonic black holes and conservation of baryon number in systems with black holes
  7. Mapping between skyrmion black holes and baryonic black holes
  8. Conservation of baryon number and folk theorems
  9. Conservation of baryon number in systems with black holes
  10. The setup
  11. The Gedankenexperiment $I$
  12. The Gedankenexperiment $II$: Monitoring Baryon/Skyrmion Hair by a Topological Surface Integral
  13. The Gedankenexperiment $III$: Monitoring Baryon/Skyrmion Hair by a Spectator Field
  14. Consequences for weak gravity conjecture
  15. Geodesic motion and scattering cross sections using the glory approximation
  16. ...and 7 more sections

Figures (17)

  • Figure 1: Profile function $F(x)$ for the case $\beta = 0$ and $m_{ADM} = 0.065$
  • Figure 2: $m(x)$ for the case $\beta = 0$ and $m_{ADM} = 0.065$
  • Figure 3: Profile function $F(x)$ for the case $\alpha = 0.01$ and $m_{ADM} = 0.065$
  • Figure 4: $m(x)$ for the case $\alpha = 0.01$ and $m_{ADM} = 0.065$
  • Figure 5: $m(x)$ for the case $\beta = 0$ and $x_h = x_h^{max,\alpha, \beta = 0}$
  • ...and 12 more figures