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

Infinite-redshift localized states of Dirac fermions under Einsteinian gravity