Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation I

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed us to test relativistic gravity in its strong, dynamical and nonlinear regime, thus opening a new arena to confront general relativity (and modifications thereof) against observations. We consider a theory that modifies general relativity by introducing a scalar field coupled to a parity-violating curvature term, known as dynamical Chern-Simons gravity. In this theory, spinning black holes are different from their general relativistic counterparts, and can thus serve as probes of this theory. We modify the Teukolsky formalism to obtain a set of linear coupled differential equations that describe dynamical gravitational and scalar perturbations of a rotating black hole in dynamical Chern-Simons gravity to leading order in spin. In this talk, I will present the modified Teukolsky formalism and the equations describing the evolution of dynamical gravitational and scalar perturbations. Additionally, I will describe the calculation of the black hole's quasi-normal mode frequencies to leading order in spin, and compare these to previously obtained results. This formalism lays down the foundations for the general extension of the calculation of quasi-normal mode frequencies for black holes that rotate arbitrarily fast in dynamical Chern-Simons gravity, therefore extending results valid in Petrov Type D backgrounds to Petrov type I backgrounds.