Recent population synthesis simulations of Pop III stars suggest that the event rate of coalescence of \sim 30 M _ { \odot } – 30 M _ { \odot } binary black holes can be high enough for the detection by the second generation gravitational wave detectors .
The frequencies of chirp signal as well as quasinormal modes are near the best sensitivity of these detectors so that it would be possible to confirm Einstein ’ s general relativity .
Using the WKB method , we suggest that for the typical value of spin parameter a / M \sim 0.7 from numerical relativity results of the coalescence of binary black holes , the strong gravity of the black hole space-time at around the radius 2 M , which is just \sim 1.17 times the event horizon radius , would be confirmed as predicted by general relativity .
The expected event rate with the signal-to-noise ratio > 35 needed for the determination of the quasinormal mode frequency with the meaningful accuracy is 0.17 – 7.2 { events~ { } yr ^ { -1 } ~ { } ( SFR _ { p } / ( 10 ^ { -2.5 } ~ { } M _ { \odot } ~ { } yr ^ { -1 } ~ { } Mpc ^ { -3 } ) ) % } \cdot ( [ f _ { b } / ( 1 + f _ { b } ) ] / 0.33 ) where { SFR _ { p } } and { f _ { b } } are the peak value of the Pop III star formation rate and the fraction of binaries , respectively .
As for the possible optical counter part , if the merged black hole of mass M \sim 60 M _ { \odot } is in the interstellar matter with n \sim 100 ~ { } { cm ^ { -3 } } and the proper motion of black hole is \sim 1 ~ { } { km~ { } s ^ { -1 } } , the luminosity is \sim 10 ^ { 40 } ~ { } { erg~ { } s ^ { -1 } } which can be detected up to \sim 300 ~ { } { Mpc } , for example , by Subaru-HSC and LSST with the limiting magnitude 26 .