We analyze gravitationally localized states of multiple fermions with high angular momenta, in the formalism introduced by Finster, Smoller, and Yau [Phys Rev. D 59, 104020 (1999)]. We show that the resulting solitonlike wave functions can be naturally interpreted in terms of a form of self-trapping, where the fermions become localized on shells the locations of which correspond to those of "bulges" in the optical geometry created by their own energy density.

We present an analysis of excited-state solutions for a gravitationally localized system consisting of a filled shell of high-angular-momentum fermions, using the Einstein-Dirac formalism introduced by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999). We show that, even when the particle number is relatively low (N f ≥ 6), the increased nonlinearity in the system causes a significant deviation in behavior from the two-fermion case. Excited-state solutions can no longer be uniquely identified by the value of their central redshift, with this multiplicity producing distortions in the characteristic spiraling forms of the mass-radius relations. We discuss the connection between this effect and the internal structure of solutions in the relativistic regime.

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We analyze the localized states of a pair of neutral fermions interacting with a Higgs field and the metric of spacetime, extending the Einstein-Dirac formalism introduced by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)]. We demonstrate that, when the coupling between the fermions and the Higgs field is strong, there is a class of bound states in which the total (ADM) mass no longer increases proportionally to the mass of the constituent fermions. This phenomenon enables fermionic particles with much larger masses than in the Higgs-free case to form stable localized states.