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

Abstract

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 $\varphi$, 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.

14 pages, no figures, version to appear in PRD

References in corpus (10)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The effects of Chern-Simons gravity on bodies orbiting the Earth
• Kerr Black Holes are Not Unique to General Relativity
• Perturbed Kerr Black Holes can probe deviations from General Relativity
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity
• Stability of f(R) black holes
• Instability of rotating black hole in a limited form of $f(R)$ gravity
• Black hole perturbation in parity violating gravitational theories
• Deeper discussion of Schrödinger invariant and Logarithmic sectors of higher-curvature gravity

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• Onset of rotating scalarized black holes in Einstein-Chern-Simons-Scalar theory
• Black hole perturbation in nondynamical and dynamical Chern-Simons gravity
• Black holes in Gauss-Bonnet and Chern-Simons-scalar theory
• (Compactified) black branes in four dimensional f(R)-gravity
• Black hole stability in Jordan and Einstein frames
• Black branes in four-dimensional conformal equivalent theories
• Massive gravitational waves in Chern-Simons modified gravity
• Cosmological and astrophysical applications of modified theories of gravity
• Tricritical gravity waves in the four-dimensional generalized massive gravity