Perturbations of spinning black holes in dynamical Chern Simons gravity: quasinormal modes

When two black holes coalesce, the gravitational waves emitted during the ringdown phase, or the quasinormal modes (QNMs), carry essential information about the spacetime geometry and astrophysical environment around the remnant black hole. These QNMs, particularly their frequencies, are vital for investigating possible deviations from General Relativity (GR). In recent years, significant progress has been made in calculating QNM frequencies in theories beyond GR. The development of the modified Teukolsky formalism further enables calculating QNMs for beyond-GR BHs with a general spin. Last year, we introduced how to apply this formalism to derive a radial master equation for the Weyl scalar ψ₀ (or ψ₄), coupled to another radial equation of the scalar field, in dynamical Chern-Simons (dCS) gravity in the slow-rotation limit. In this talk, I will show how to extract the QNM frequencies from this set of equations. We will first show that the even- and odd-parity modes decouple, with the scalar field coupled to the odd-parity modes only, consistent with the previous findings using metric perturbations. We then solve for the scalar field using Green’s function and plug the result into the modified Teukolsky equation. In the end, we transform this equation to a quantum-mechanical eigenvalue problem to compute the QNM frequencies, comparing our results with those derived from metric perturbations.