Abstract
We perform the stability analysis of the Schwarzschild black hole in gravity with the parity-violating Chern–Simons (CS) term coupled to a dynamical scalar field . For this purpose, we transform the gravity into the scalar-tensor theory by introducing a scalaron , providing the dynamical CS modified gravity with two scalars. The perturbation equation for the scalar 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 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.
- Received 14 September 2011
DOI:https://doi.org/10.1103/PhysRevD.84.104029
© 2011 American Physical Society