Quasi-normal modes of hairy scalar tensor black holes: odd parity

The odd parity gravitational quasi-normal mode spectrum of black holes with non-trivial scalar hair in Horndeski gravity is investigated. We study 'almost' Schwarzschild black holes such that any modifications to the spacetime geometry (including the scalar field profile) are treated as small quantities. A modified Regge-Wheeler style equation for the odd parity gravitational degree of freedom is presented to quadratic order in the scalar hair and spacetime modifications, and a parameterisation of the modified quasi-normal mode spectrum is calculated. In addition, statistical error estimates for the new hairy parameters of the black hole and scalar field are given.