Perturbations of Schwarzschild black holes in dynamical Chern-Simons modified gravity

Dynamical Chern-Simons modified gravity is an attractive, yet relatively unexplored, candidate to an alternative theory of gravity. The dynamical Chern-Simons correction couples a dynamical scalar field to the gravitational field. In this framework, we analyze the perturbation formalism and stability properties of spherically symmetric black holes. Assuming that no background scalar field is present, gravitational perturbations with polar and axial parities decouple. We find no effect of the Chern-Simons coupling on the polar sector, while axial perturbations couple to the Chern-Simons scalar field. The axial sector can develop strong instabilities if the coupling parameter beta, associated to the dynamical coupling of the scalar field, is small enough; this yields a constraint on beta which is much stronger than the constraints previously known in the literature.