Stability of Schwarzschild black hole in f(R) gravity with the dynamical Chern-Simons term

Details Stability of Schwarzschild black hole in f(R) gravity with the dynamical Chern-Simons term Stability of Schwarzschild black hole in f(R) gravity with the dynamical Chern-Simons term

2011-09-13

arxiv.org/abs/1109.2719v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, no figures, version to appear in PRD

Scientific paper

We perform the stability analysis of the Schwarzschild black hole in $f(R)$ gravity with the parity-violating Chern-Simons (CS) term coupled to a dynamical scalar field $\theta$. For this purpose, we transform the $f(R)$ gravity into the scalar-tensor theory by introducing a scalaron $\phi$, providing the dynamical Chern-Simons modified gravity with two scalars. The perturbation equation for the scalar $\theta$ is coupled to the odd-parity metric perturbation equation, providing a system of two coupled second order equations, while the scalaron is coupled to the even-parity perturbation equation. This implies that the CS coupling affects the Regge-Wheeler equation, while $f(R)$ gravity does not affect the Zerilli equation. It turns out that the Schwarzschild black hole is stable against the external perturbations if the scalaron is free from the tachyon.

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