On the stability of spherically symmetric spacetimes in metric f(R) gravity

TL;DR

This paper investigates the stability of spherically symmetric star spacetimes in metric f(R) gravity, revealing constraints on models that match observed gravitational parameters and highlighting naturalness issues for models explaining cosmic acceleration.

Contribution

It analyzes how stability depends on specific models and configurations in metric f(R) gravity, emphasizing stability constraints and naturalness problems.

Findings

Configurations with b3_{PPN} b1 1 are highly constrained.

Configurations with b3_{PPN} b1 1/2 are less constrained.

Stable solutions often have a very limited phase space.

Abstract

We consider stability properties of spherically symmetric spacetimes of stars in metric f(R) gravity. We stress that these not only depend on the particular model, but also on the specific physical configuration. Typically configurations giving the desired $\gamma_{\rm PPN} \approx 1$ are strongly constrained, while those corresponding to $\gamma_{\rm PPN} \approx 1/2$ are less affected. Furthermore, even when the former are found strictly stable in time, the domain of acceptable static spherical solutions typically shrinks to a point in the phase space. Unless a physical reason to prefer such a particular configuration can be found, this poses a naturalness problem for the currently known metric f(R) models for accelerating expansion of the Universe.