Rastall’s theory of gravity: spherically symmetric solutions and the stability problem

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. The analysis of perturbations shows that there arises an inconsistency in the sense that time-dependent perturbations do not exist in any order of perturbation theory, and we can conclude that these solutions are pertubatively stable (though nonperturbative time-dependent solutions are not excluded). Possible reasons for this inconsistency are discussed. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.