Stability of black holes in f(R) gravity

Abstract

We investigate the stability of black holes in the viable model of $f(R)=R+R^2$ gravity which was known to be the best fit for inflation. These include Schwarzschild and Kerr black holes. Instead of studying the fourth-order linearized equation around the black hole background, we use the corresponding tensor-scalar theory of the Starobinsky model to perform their stability. The Schwarzschild black hole is stable, while the Kerr black hole is unstable because of superradiant instability.

1+13 pages, 2 figures

References in corpus (5)

• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Superradiant instabilities in astrophysical systems
• Higher dimensional charged $f(R)$ black holes
• Kerr Black Holes are Not Unique to General Relativity
• Consistency relation for $R^p$ inflation