Evolving metric perturbations in dynamical Chern-Simons gravity

The stability of rotating black holes in dynamical Chern-Simons gravity (dCS) is an open question. To study this issue, we evolve the leading-order metric perturbation in order-reduced dynamical Chern-Simons gravity. The source is the leading-order dCS scalar field coupled to the spacetime curvature of a rotating black hole background. We use a well-posed, constraint-preserving scheme. We find that the leading-order metric perturbation numerically exhibits linear growth, but that the level of this growth converges to zero with numerical resolution. This analysis shows that spinning black holes in dCS gravity are numerically stable to leading-order perturbations in the metric.