Non-Existence of Black Hole Solutions to Static, Spherically Symmetric Einstein-Dirac Systems - a Critical Discussion

TL;DR

This paper critically examines various proof methods and concludes that static, spherically symmetric Einstein-Dirac systems do not admit solutions, highlighting the non-existence of such configurations.

Contribution

It provides a comparative analysis of proof techniques demonstrating the non-existence of static, spherically symmetric solutions in Einstein-Dirac systems.

Findings

Multiple proof methods confirm non-existence

No static, spherically symmetric Einstein-Dirac solutions exist

Clarifies limitations of solution existence in Einstein-Dirac models

Abstract

This short note compares different methods to prove that Einstein-Dirac systems have no static, spherically symmetric solutions.