Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasinormal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasinormal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins J=M2 -0.7. In this article, we compute for the first time the gravitational quasinormal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pade ' resummation of the quasinormal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins -0.7; therefore, our results can be used in the data analysis of ringdown signals.