The evolution of the spin and tilt of black holes in compact black hole - neutron star and black hole - black hole binary systems is investigated within the framework of the coalescing compact star binary model for short gamma ray bursts via the population synthesis method .
Based on recent results on accretion at super critical rates in slim disk models , estimates of natal kicks , and the results regarding fallback in supernova models , we obtain the black hole spin and misalignment .
It is found that the spin parameter , a _ { spin } , is less than 0.5 for initially non rotating black holes and the tilt angle , i _ { tilt } , is less than 45 ^ { \circ } for 50 % of the systems in black hole - neutron star binaries .
Upon comparison with the results of black hole - neutron star merger calculations we estimate that only a small fraction ( \sim 0.01 ) of these systems can lead to the formation of a torus surrounding the coalesced binary potentially producing a short-hard gamma ray burst .
On the other hand , for high initial black hole spin parameters ( a _ { spin } > 0.6 ) this fraction can be significant ( \sim 0.4 ) .
It is found that the predicted gravitational radiation signal for our simulated population does not significantly differ from that for non rotating black holes .
Due to the ( i ) insensitivity of signal detection techniques to the black hole spin and the ( ii ) predicted overall low contribution of black hole binaries to the signal we find that the detection of gravitational waves are not greatly inhibited by current searches with non spinning templates .
It is pointed out that the detection of a black hole - black hole binary inspiral system with LIGO or VIRGO may provide a direct measurement of the initial spin of a black hole .