Infinite-redshift localized states of Dirac fermions under Einsteinian gravity

Abstract

We present a set of localized states for an even number of Dirac fermions under Einsteinian gravity that have an infinite central redshift. Near the center of the localized state the components of the Dirac spinor and the spacetime metric all show simple power-law dependences on the radial distance; further out the fermionic wave function decays to zero and the spacetime becomes asymptotically flat. We show that this `central' solution of the equations of motion can be used to understand much of the structure observed by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] in their numerical solutions of the same problem at finite central redshift.

arXiv comment14 pages, 10 figures

References in corpus (5)

• The Dynamics of General Relativity
• Particle-Like Solutions of the Einstein-Dirac Equations
• Particle-Like Solutions of the Einstein-Dirac-Maxwell Equations
• Non-Existence of Black Hole Solutions for a Spherically Symmetric, Static Einstein-Dirac-Maxwell System
• The Coupling of Gravity to Spin and Electromagnetism

Cited by in corpus (5)

• Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons
• Einstein-Dirac system in semiclassical gravity
• Gravitationally localized states of two neutral fermions interacting with a Higgs field
• Self-gravitating nonlinear Dirac fields
• 'Stealth' singularities from self-gravitating fermions