The dynamical stability of the static real scalar field solutions to the Einstein-Klein-Gordon equations revisited

TL;DR

This paper revisits the stability of static scalar field solutions in Einstein-Klein-Gordon systems, correcting previous proofs and showing some solutions are actually stable under perturbations.

Contribution

It provides a corrected analysis of the stability of these solutions and demonstrates the existence of perturbatively stable solutions.

Findings

Previous instability proofs were corrected.

Some static solutions are shown to be perturbatively stable.

The stability landscape of Einstein-Klein-Gordon solutions is clarified.

Abstract

We re-examine the dynamical stability of the nakedly singular, static, spherical ly symmetric solutions of the Einstein-Klein Gordon system. We correct an earlier proof of the instability of these solutions, and demonstrate that there are solutions to the massive Klein-Gordon system that are perturbatively stable.