Abstract
The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than $50\%$ of the ergoregion by the second generation gravitational wave detectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odot yr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively.
Highlights
The Kerr space-time [1] is unique in two senses
III (Pop III) binary black holes, we find that the peak of the final merger mass (M f ) is about
The standard model of Population III (Pop III) population synthesis tells us that the event rate for the confirmation of more than 50% of the ergoregion by second generation gravitational wave detectors is ∼2.3 events yr−1 (SFRp /(10−2.5 M yr−1 Mpc−3 )) · ([fb /(1 + fb )]/0.33), where SFRp and fb are the peak value of the Pop III star formation rate and the fraction of binaries, respectively
Summary
The existence of the ergoregion of the Kerr space-time has not yet been confirmed observationally. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. 50 M , while the fraction of the final spin q f = a f /M f > 0.7 needed for the confirmation of a part of the ergoregion is ∼77%. To confirm the frequency of the quasinormal mode, SNR > 35 is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than 50% of the ergoregion by second generation gravitational wave detectors is ∼2.3 events yr−1 (SFRp /(10−2.5 M yr−1 Mpc−3 )) · ([fb /(1 + fb )]/0.33), where SFRp and fb are the peak value of the Pop III star formation rate and the fraction of binaries, respectively
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