Higher Harmonic Spin-Precession Gravitational Waveforms in Dynamical Chern-Simons

In dynamical Chern-Simons (dCS) theory the no-hair theorem of vacuum solutions to general relativity (GR) is violated. Within GR multipolar structures of the exterior spacetime are fixed to depend only on the mass and spin of a Kerr black hole (the no-hair theorem). Yet, in parity-violating theories, such as dCS, these structures have alternative multipolar arrangements. Here the beyond-GR corrections in dCS have dependencies on the relation between the spin of the compact objects and orbital angular momentum of the binary system. In the non-spinning limit, corrections to GR occur at higher post-Newtonian order. Thus, to identify leading-order, beyond-GR corrections in realistic black hole binaries a spin-precession parameterized post-Einsteinian (ppE) waveform is necessary. This will lead to precession phase and spectral amplitude modulations, along with beyond-GR corrections, in typical ppE waveforms that would also require higher harmonics. This talk will discuss a model incorporating higher harmonics in existing spin-precession waveforms to perform tests of GR with current and future detectors.