Effective Field Theory of Black Hole Quasinormal Modes in Scalar-Tensor
  Theories
  The final ringdown phase in a coalescence process is a valuable laboratory to
test General Relativity and potentially constrain additional degrees of freedom
in the gravitational sector. We introduce here an effective description for
perturbations around spherically symmetric spacetimes in the context of
scalar-tensor theories, which we apply to study quasi-normal modes for black
holes with scalar hair. We derive the equations of motion governing the
dynamics of both the polar and the axial modes in terms of the coefficients of
the effective theory. Assuming the deviation of the background from
Schwarzschild is small, we use the WKB method to introduce the notion of "light
ring expansion". This approximation is analogous to the slow-roll expansion
used for inflation, and it allows us to express the quasinormal mode spectrum
in terms of a small number of parameters. This work is a first step in
describing, in a model independent way, how the scalar hair can affect the
ringdown stage and leave signatures on the emitted gravitational wave signal.
Potential signatures include the shifting of the quasi-normal spectrum, the
breaking of isospectrality between polar and axial modes, and the existence of
scalar radiation.
