On the stability of electrovacuum space-times in scalar-tensor gravity

TL;DR

This paper investigates the stability of static, spherically symmetric electrovacuum solutions in various scalar-tensor theories of gravity, analyzing how boundary conditions influence their potential stability or instability.

Contribution

It provides a unified stability analysis for multiple scalar-tensor theories using conformal transformations and introduces physically motivated boundary conditions for solutions with naked singularities.

Findings

Stability depends on boundary conditions and specific solution branches.

All studied theories reduce to a common wave equation for perturbations.

Results are summarized in a comprehensive stability table.

Abstract

We study the behavior of static, spherically symmetric solutions to the field equations of scalar-tensor theories (STT) of gravity belonging to the Bergmann-Wagoner-Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans-Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter $\xi$. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.