Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons

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