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

TL;DR

This paper investigates how nonlinear effects influence the excited states of many-fermion Einstein-Dirac solitons, revealing complex behaviors and deviations from simpler two-fermion models due to increased nonlinearity.

Contribution

It demonstrates that higher particle numbers lead to non-uniqueness in excited-state solutions and distortions in mass-radius relations, advancing understanding of nonlinear gravitational fermion systems.

Findings

Nonlinearity causes significant deviations from two-fermion behavior.

Excited states are no longer uniquely identified by central redshift.

Mass-radius relations exhibit distorted spirals due to nonlinearity.

Abstract

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 ($N_f\ge 6$), 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.