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The existence of the ergoregion of the Kerr space-time has not been confirmedobservationally yet. We show that the confirmation would be possible byobserving the quasinormal mode in gravitational waves. As an example, using therecent population synthesis results of Pop III binary black holes, we find thatthe peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, whilethe fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for theconfirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequencyof the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of PopIII population synthesis tells us that the event rate for the confirmation ofmore than $50\%$ of the ergoregion by the second generation gravitational wavedetectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odotyr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and${\rm f_b}$ are the peak value of the Pop III star formation rate and thefraction of binaries, respectively.

Possible confirmation of the existence of ergoregion by the Kerr quasinormal mode in gravitational waves from Pop III massive black hole binary