Stability of f(R) black holes

TL;DR

This paper analyzes the stability of $f(R)$ gravity black holes by transforming the theory into a scalar-tensor form, demonstrating stability when the scalaron mass is non-tachyonic.

Contribution

It introduces a method to analyze $f(R)$ black hole stability by converting it into a second-order scalar-tensor theory, simplifying perturbation analysis.

Findings

$f(R)$ black holes are stable if the scalaron mass is non-tachyonic.

Transformation to scalar-tensor theory reduces perturbation equations to second order.

Stability depends on the scalaron mass condition.

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.