  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 which 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 to this theory. We study linear gravito-scalar perturbations of black
holes in dynamical Chern-Simons gravity at leading-order in spin and (i) obtain
the perturbed field equations describing the evolution of the perturbed
gravitational and scalar fields, (ii) numerically solve these equations by
direct integration to calculate the quasinormal mode frequencies for the
dominant and higher multipoles and tabulate them, (iii) find strong evidence
that these rotating black holes are linearly stable, and (iv) present general
fitting functions for different multipoles for gravitational and scalar
quasinormal mode frequencies in terms of spin and Chern-Simons coupling
parameter. Our results can be used to validate the ringdown of small-spin
remnants of numerical relativity simulations of black hole binaries in
dynamical Chern-Simons gravity and pave the way towards future tests of this
theory with gravitational wave ringdown observations.
