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

Abstract

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. As an example, using the recent population synthesis results of Population III (Pop III) binary black holes, we find that the peak of the final merger mass (Mf ) is about 50M⊙, while the fraction of the final spin q f = af/Mf > 0.7 needed for the confirmation of a part of the ergoregion is∼77%. To confirmthe frequency of the quasinormalmode, 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/(10-2.5M⊙ 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.