Schwarzschild-f(R) Black Holes and the Absence of Black Hole Bomb Effect

TL;DR

This paper analytically demonstrates that Schwarzschild-f(R) black holes are stable against superradiant charged scalar perturbations, indicating they do not exhibit the black hole bomb effect, extending stability analysis methods to modified gravity black holes.

Contribution

The study extends superradiant stability analysis to Schwarzschild-f(R) black holes using an analytic approach, showing their stability and absence of the black hole bomb effect.

Findings

Schwarzschild-f(R) black holes are superradiantly stable.

No black hole bomb effect occurs in these black holes.

Analytic methods from higher-dimensional black hole studies are successfully applied.

Abstract

In this paper, we analytically study the superradiant stability of Schwarzschild-f(R) black holes under charged massive scalar perturbation. Using an analytic method based on Descartes' rule of signs, we extend previous methods developed for higher-dimensional Reissner-Nordstrom black holes to the Schwarzschild-f(R) black hole cases. Our results show that Schwarzschild-f(R) black holes are superradiantly stable under charged massive scalar perturbation, implying the absence of the black hole bomb effect.