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

TL;DR

This paper proposes that observing quasinormal modes in gravitational waves from Pop III black hole mergers could confirm the existence of the ergoregion in Kerr spacetime, with specific event rate estimates for future detectors.

Contribution

It demonstrates a method to confirm the ergoregion via gravitational wave observations of Pop III black hole mergers, providing event rate estimates for such detections.

Findings

Peak final merger mass around 50 solar masses.

Fraction of final spin > 0.7 needed for ergoregion confirmation.

Event rate estimated at approximately 2.3 events per year.

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.