Perturbations of spinning black holes in dynamical Chern-Simons gravity II: master equations

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and therefore their merger may lead to a modified ringdown spectrum. Last year, we developed a new formalism to derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $Psi_0$ and $Psi_4$. In this talk, I will focus on: (1) applying our new formalism to slowly rotating black holes in dynamical Chern-Simons gravity; (2) present the master equation in the null tetrad basis; (3) discuss the application of metric reconstruction and perturbation scheme procedures involved in decomposing the master equation to the coordinate basis; (4) and lastly, present the master equations in terms of the radial and angular coordinates. These equations can then be integrated to obtain the QNM spectra. Our work enables the calculation of the QNM spectra, thus laying the foundations to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin.