Infinite-redshift localized states of Dirac fermions under Einsteinian gravity

TL;DR

This paper introduces a class of localized Dirac fermion states in Einsteinian gravity with infinite central redshift, revealing their structure and relation to previous numerical solutions at finite redshift.

Contribution

It provides an analytical description of infinite-redshift localized states of Dirac fermions under Einsteinian gravity, linking them to earlier numerical findings.

Findings

Components show power-law dependence near the center

Fermionic wave function decays outward

Spacetime becomes asymptotically flat

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.