The gravitational waveforms in the ghost-free bigravity theory exhibit deviations from those in general relativity. The main difference is caused by graviton oscillations in the bigravity theory. We investigate the prospects for the detection of the
corrections to gravitational waveforms from coalescing compact binaries due to graviton oscillations and for constraining bigravity parameters with the gravitational wave observations. We consider the bigravity model discussed by the De Felice-Nakamura-Tanaka subset of the bigravity model, and the phenomenological model in which the bigravity parameters are treated as independent variables. In both models, the bigravity waveform shows strong amplitude modulation, and there can be a characteristic frequency of the largest peak of the amplitude, which depends on the bigravity parameters. We show that there is a detectable region of the bigravity parameters for the advanced ground-based laser interferometers, such as Advanced LIGO, Advanced Virgo, and KAGRA. This region corresponds to the effective graviton mass of $mu geq 10^{-17}~{rm cm}^{-1}$ for $tilde{c}-1 geq 10^{-19}$ in the phenomenological model, while $mu geq 10^{-16.5}~{rm cm}^{-1}$ for $kappaxi_c^2 geq 10^{0.5}$ in the De Felice-Nakamura-Tanaka subset of the bigravity model, respectively, where $tilde{c}$ is the propagation speed of the massive graviton and $kappaxi_c^2$ corresponds to the corrections to the gravitational constant in general relativity. These regions are not excluded by existing solar system tests. We also show that, in the case of $1.4-1.4M_{rm sun}$ binaries at the distance of $200~{rm Mpc}$, $logmu^2$ is determined with an accuracy of ${cal O}$(0.1)% at the 1$sigma$ level for a fiducial model with $mu^2=10^{-33}~{rm cm}^{-2}$ in the case of the phenomenological model.
The cross-correlation search has been previously applied to map the gravitational wave (GW) stochastic background in the sky and also to target GW from rotating neutron stars/pulsars. Here we investigate how the cross-correlation method can be used t
o target a small region in the sky spanning at most a few pixels, where a pixel in the sky is determined by the diffraction limit which depends on the (i) baseline joining a pair of detectors and (ii) detector bandwidth. Here as one of the promising targets, we consider the Virgo cluster - a hot spot spanning few pixels - which could contain, as estimates suggest $sim 10^{11}$ neutron stars, of which a small fraction would continuously emit GW in the bandwidth of the detectors. For the detector baselines, we consider advanced detector pairs among LCGT, LIGO, Virgo, ET etc. Our results show that sufficient signal to noise can be accumulated with integration times of the order of a year. The results improve for the multibaseline search. This analysis could as well be applied to other likely hot spots in the sky and other possible pairs of detectors.
Recently, Banados, Silk and West (BSW) showed that the total energy of two colliding test particles has no upper limit in their center of mass frame in the neighborhood of an extreme Kerr black hole, even if these particles were at rest at infinity i
n the infinite past. We call this mechanism the BSW mechanism or BSW process. The large energy of such particles would generate strong gravity, although this has not been taken into account in the BSW analysis. A similar mechanism is seen in the collision of two spherical test shells in the neighborhood of an extreme Reissner-Nordstrom black hole. In this paper, in order to draw some implications concerning the effects of gravity generated by colliding particles in the BSW process, we study a collision of two spherical dust shells, since their gravity can be exactly treated. We show that the energy of two colliding shells in the center of mass frame observable from infinity has an upper limit due to their own gravity. Our result suggests that an upper limit also exists for the total energy of colliding particles in the center of mass frame in the observable domain in the BSW process due the gravity of the particles.
