Rastall's theory of gravity: Spherically symmetric solutions and the stability problem

TL;DR

This paper investigates the stability of static, spherically symmetric solutions in Rastall's gravity with scalar fields, finding that linear perturbations cannot exist, implying these solutions are stable, though the analysis has inconsistencies.

Contribution

It reveals an inconsistency in the stability analysis of Rastall's solutions, suggesting they are stable under spherically symmetric perturbations despite methodological issues.

Findings

Linear perturbations cannot exist in the analysis.

Solutions are concluded to be stable.

Discussion of potential reasons for the inconsistency.

Abstract

We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the sense that linear time-dependent perturbations cannot exist, and we can conclude that these solutions are stable. Possible reasons for this inconsistency are discussed.