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

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.

18 pages, 12 figures

References in corpus (5)

• Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions
• Excited Boson Stars
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Fermion self-trapping in the optical geometry of Einstein-Dirac solitons
• Infinite-redshift localized states of Dirac fermions under Einsteinian gravity

Cited by in corpus (7)

• Fermion soliton stars
• Dirac-boson stars
• Einstein-Dirac system in semiclassical gravity
• Time-dependent Spinor field in a static cylindrically-symmetric space-time
• Gravitationally localized states of two neutral fermions interacting with a Higgs field
• Self-gravitating nonlinear Dirac fields
• 'Stealth' singularities from self-gravitating fermions