Stability of f(R) black holes

Abstract

We investigate the stability of $f(R)$ (Schwarzschild) black hole obtained from the $f(R)$ gravity. It is difficult to carry out the perturbation analysis around the black hole because the linearized Einstein equation is fourth order in $f(R)$ gravity. In order to resolve this difficulty, we transform $f(R)$ gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a scalaron, showing that all linearized equations are second order, which are the same equations for the massive Brans-Dicke theory. It turns out that the $f(R)$ black hole is stable against the external perturbations if the scalaron does not have a tachyonic mass.

16 pages, no figures, version to appear in Physical Review D

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Cited by in corpus (5)

• Instabilities and Anti-Evaporation of Reissner-Nordström Black Holes in modified $F(R)$ gravity
• Accretion disks around black holes in modified strong gravity
• Stability of Schwarzschild singularity in non-local gravity
• Weak-field limit of f(R)-gravity in three and more spatial dimensions
• Propagating degrees of freedom in f(R) gravity