Possible golden events for ringdown gravitational waves

Abstract: There is a forbidden region in the parameter space of quasinormal modes of black holes in general relativity. Using both inspiral and ringdown phases of gravitational waves from binary black holes, we propose two methods to test general relativity. We also evaluate how our methods will work when we apply them to Pop III black-hole binaries with typical masses. Adopting the simple mean of the estimated range of the event rate, we have the expected rate of 500 ${\rm yr^{-1}}$. Then, the rates of events with signal-to-noise ratios greater than 20 and greater than 50 are 32 ${\rm yr^{-1}}$ and 2 ${\rm yr^{-1}}$, respectively. Therefore, there is a good chance to confirm (or refute) the Einstein theory in the strong gravity region by observing the expected quasinormal modes.