Correlation between gravitational wave frequencies as a signature of new black hole physics

We point out that for black holes (BH) of the same mass, despite of arising from two entirely different physical arguments, the peak frequency of the coarse-grained gravitational wave (GW) spectrum of gravitons f peak graviton is very close to the peak frequency of the GW spectrum produced from binary BH mergers f peak merger. In particular, we find that f peak graviton/f peak merger about 2.3 independent from BH mass or population. If BHs are still evaporating, the peak frequencies scale as proportional to M i-1 with M i is the initial BH mass. If BHs evaporated in the radiation (matter) dominated era, the peak frequencies scale as proportional to M i 1/2 (proportional to M i) respectively after taking into account redshift effect. Any deviation from the aforementioned magical ratio would indicate new BH physics. The sweetest frequency ballpark to look for this correlation is around 10 14 Hz-10 20 Hz where both GW spectra are allowed to have maximum amplitude. As a demonstration of what the new physics could be, we consider a phenomenological self-similar regular BH model of Hayward featuring a single hair parameter. The observed ratio of peak frequencies can be used to directly infer the hair parameter, along with crucial properties of the novel BH solution such as Hawking temperature, horizon size, and innermost stable circular orbit. We also comment on the pros and cons of correlating frequencies among other GW sources such as formation, population fluctuation, and sudden transition of adiabatic perturbation.