Stability analysis of f(R)-AdS black holes

TL;DR

This paper investigates the stability of f(R)-AdS black holes by transforming the problem into a scalar-tensor theory, analyzing the scalaron dynamics, and confirming stability through potential positivity and quasinormal mode calculations.

Contribution

It introduces a method to analyze f(R)-AdS black hole stability by converting to scalar-tensor form and applying the S-deformed technique, providing new stability criteria.

Findings

Stability guaranteed if scalaron mass squared meets Breitenlohner-Freedman bound.

All linearized equations reduced to second order.

Quasinormal frequencies support stability conclusions.

Abstract

We study the stability of f(R)-AdS (Schwarzschild-AdS) black hole obtained from f(R) gravity. In order to resolve the difficulty of solving fourth order linearized equations, we transform f(R) gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a dynamical scalaron, showing that all linearized equations are second order. Using the positivity of gravitational potentials and S-deformed technique allows us to guarantee the stability of f(R)-AdS black hole if the scalaron mass squared satisfies the Breitenlohner-Freedman bound. This is confirmed by computing quasinormal frequencies of the scalaron for large f(R)-AdS black hole.