'Stealth' singularities from self-gravitating fermions

TL;DR

This paper introduces an analytic solution to Einstein-Dirac equations describing localized fermion states with a naked singularity and zero gravitational mass, suggesting a new way mass could be hidden in the universe.

Contribution

It provides the first analytic solution with a naked singularity and zero ADM mass for self-gravitating fermions, expanding understanding of possible fermionic gravitational configurations.

Findings

Solution features a naked singularity at the origin.

Localized fermion wavefunction is normalizable and exponentially localized.

The gravitational mass of the configuration is zero despite large fermion mass.

Abstract

We present a new analytic solution to the Einstein-Dirac equations formulated by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] to describe the stationary states of a pair of gravitationally interacting neutral fermions. The fermions' wavefunction in our analytic solution, as in their numerical ones, is both exponentially localized and normalizable. However, our solution differs from theirs in two key respects: it features a naked spacetime singularity at the origin, and the gravitational (Arnowitt-Deser-Misner) mass of the localized object is zero, making it gravitationally undetectable to an external observer. This is despite the arbitrarily large mass of the constituent fermions. This unexpected result may have significant implications for astronomy and cosmology, as it gives a mechanism by which mass could become 'hidden' during the universe's evolution.