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

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 ${\gamma }_{\mathrm{PPN}}\approx 1$ are strongly constrained, while those corresponding to ${\gamma }_{\mathrm{PPN}}\approx 1/2$ 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.

arXiv commentPublished version, 9 pages, 3 figures

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• A Singularity Problem with f(R) Dark Energy
• Initial and final de Sitter universes from modified $f(R)$ gravity
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• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
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• How delicate are the $f(R)$ gravity models with disappearing cosmological constant?
• Small Cosmological Constant from Running Gravitational Coupling