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Stability of f(R) black holes

Yun Soo Myung1,*, Taeyoon Moon2,†, and Edwin J. Son2,‡

  • 1Institute of Basic Sciences and School of Computer Aided Science, Inje University, Gimhae 621-749, Korea
  • 2Center for Quantum Space-time, Sogang University, Seoul, 121-742, Korea

  • *ysmyung@inje.ac.kr
  • †tymoon@sogang.ac.kr
  • ‡eddy@sogang.ac.kr
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Phys. Rev. D 83, 124009 – Published 2 June, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.124009

Abstract

We investigate the stability of an 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.

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Phys. Rev. D 83, 124009– Published 2 June, 2011
  • Received 3 March 2011

© 2011 American Physical Society

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