Determine the extent of the negative-ADM-mass region

Determine how far the region of negative ADM mass extends in the gravitating chiral-quark soliton model, including how its extent depends on the Dirac-sea contribution, the regularization scheme, and the cutoff used to regularize the infinite sum of Dirac eigenstates.

Background

The paper finds self-consistent gravitating chiral-quark soliton solutions whose ADM mass can become negative as the dynamical mass increases. The authors attribute this behavior to an excess of the regularized Dirac-sea contribution over the valence contribution.

Because the Dirac-sea energy depends on the regularization prescription and cutoff, the range of parameters supporting negative ADM mass is not established. The authors identify determining the extent of this region as the most crucial unresolved question.

References

The most crucial question is how far the ADM negative mass region spans; this depends on the excess of the Dirac-sea, that is, the regularization scheme and the cutoff value chosen to regularize the infinite sum of the Dirac eigenstates.

— Soliton solution of a gravitating chiral-quark soliton model: dynamical fermion and Dirac-sea in general relativity  (2609.24159 - Mizutani et al., 21 Sep 2026) in Section 5, Summary

The following open problems should be resolved in future research. Our result is the regularization scheme dependent. The proper-time regularization scheme has been mostly used in the chiral-quark soliton model in flat spacetime. However, in order to verify the validity found in this paper, we should employ an alternative scheme, such as the Pauli-Villars method.

— Soliton solution of a gravitating chiral-quark soliton model: dynamical fermion and Dirac-sea in general relativity  (2609.24159 - Mizutani et al., 21 Sep 2026) in Section 5, Summary