Gravitating Skyrmions with localized fermions

TL;DR

This paper explores how Dirac fermions influence self-gravitating Skyrmions, revealing that fermion backreaction can alter configurations and lead to solutions with negative ADM mass.

Contribution

It investigates the impact of fermion backreaction on self-gravitating Skyrmions, including the emergence of anti-gravitating solutions with negative mass.

Findings

Fermion backreaction significantly affects Skyrmion configurations.

Regular solutions with negative ADM mass can occur due to fermion influence.

Fermion spectral flow is affected by gravitational and Yukawa couplings.

Abstract

We consider self-gravitating Skyrmions in the presence of Dirac fermions, that carry spin and isospin. By varying the gravitational and the Yukawa coupling constants, we investigate the spectral flow of the fermion eigenvalue associated with a zero mode in the absence of gravity. We demonstrate that the backreaction of the fermion can strongly influence the Skyrmion-fermion configurations. In particular, the energy conditions may be violated, and regular anti-gravitating asymptotically flat solutions with negative ADM mass may emerge.