We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and approximate algebr
aic Petrov types in the strong field regime. We define an index $mathcal{D}=sqrt{12/I}left(Psi_2 - Psi_3^2/Psi_4right)$ able to discriminate between Petrov types II and D and define regions of spacetime of those approximate types when used in conjunction with the speciality invariant $S=27J^2/I^3$. We provide an explicit example applying this method to Brill-Lindquist initial data corresponding to two nonspinning black holes from rest at a given initial separation. We find a doughnut-like region that is approximately of Petrov type II surrounded by an approximately Petrov type D region. We complete the study by proposing a totally symmetric tetrad fixing of the transverse frame that can be simply implemented in numerically generated spacetimes through the computation of spin coefficients ratios. We provide an application by explicitly deriving the Kerr-perturbative equations in this tetrad.
We have examined gravitational wave echo signals for nine binary black hole merger events observed by Advanced LIGO and Virgo during the first and second observation runs. To construct an echo template, we consider Kerr spacetime, where the event hor
izon is replaced by a reflective membrane. We use frequency-dependent reflection rate at the angular potential barrier, which is fitted to the numerical data obtained by solving Teukolsky equations. This reflection rate gives a frequency-dependent transmission rate that is suppressed at lower frequencies in the template. We also take into account the overall phase shift of the waveform as a parameter, which arises when the wave is reflected at the membrane and potential barrier. Using this template based on black hole perturbation, we find no significant echo signals in the binary black hole merger events.
It is known that a quasinormal mode (QNM) of a remnant black hole dominates a ringdown gravitational wave (GW) in a binary black hole (BBH) merger. To study properties of the QNMs, it is important to determine the time when the QNMs appear in a GW si
gnal as well as to calculate its frequency and amplitude. In this paper, we propose a new method of estimating the starting time of the QNM and calculating the QNM frequency and amplitude of BBH GWs. We apply it to simulated merger waveforms by numerical relativity and the observed data of GW150914. The results show that the obtained QNM frequencies and time evolutions of amplitudes are consistent with the theoretical values within 1% accuracy for pure waveforms free from detector noise. In addition, it is revealed that there is a correlation between the starting time of the QNM and the spin of the remnant black hole. In the analysis of GW150914, we show that the parameters of the remnant black hole estimated through our method are consistent with those given by LIGO and a reasonable starting time of the QNM is determined.
In the population synthesis simulations of Pop III stars, many BH (Black Hole)-BH binaries with merger time less than the age of the Universe $(tau_{rm H})$ are formed, while NS (Neutron Star)-BH binaries are not. The reason is that Pop III stars hav
e no metal so that no mass loss is expected. Then, in the final supernova explosion to NS, much mass is lost so that the semi major axis becomes too large for Pop III NS-BH binaries to merge within $tau_{rm H}$. However it is almost established that the kick velocity of the order of $200-500{rm~ km~s^{-1}}$ exists for NS from the observation of the proper motion of the pulsar. Therefore, the semi major axis of the half of NS-BH binaries can be smaller than that of the previous argument for Pop III NS-BH binaries to decrease the merging time. We perform population synthesis Monte Carlo simulations of Pop III NS-BH binaries including the kick of NS and find that the event rate of Pop III NS-BH merger rate is $sim 1 {rm Gpc^{-3} yr^{-1}}$. This suggests that there is a good chance of the detection of Pop III NS-BH mergers in O2 of Advanced LIGO and Advanced Virgo from this autumn.
Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{rm events~yr^{-1}}~({rm SFR_p}/ (10^{-2.5}~M_odot~
{rm yr^{-1}~Mpc^{-3}})) cdot ({rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${rm SFR_p}$ and ${rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{rm events~yr^{-1}}~({rm SFR_p}/ (10^{-2.5}~M_odot~{rm yr^{-1}~Mpc^{-3}})) cdot ({rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black holes spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{rm events~yr^{-1}}~({rm SFR_p}/ (10^{-2.5}~M_odot~{rm yr^{-1}~Mpc^{-3}})) cdot ({rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{rm events~yr^{-1}}~({rm SFR_p}/ (10^{-2.5}~M_odot~{rm yr^{-1}~Mpc^{-3}})) cdot ({rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.
As 2 black holes bound to each other in a close binary approach merger their inspiral time becomes shorter than the characteristic inflow time of surrounding orbiting matter. Using an innovative technique in which we represent the changing spacetime
in the region occupied by the orbiting matter with a 2.5PN approximation and the binary orbital evolution with 3.5PN, we have simulated the MHD evolution of a circumbinary disk surrounding an equal-mass non-spinning binary. Prior to the beginning of the inspiral, the structure of the circumbinary disk is predicted well by extrapolation from Newtonian results. The binary opens a low-density gap whose radius is roughly two binary separations, and matter piles up at the outer edge of this gap as inflow is retarded by torques exerted by the binary; nonetheless, the accretion rate is diminished relative to its value at larger radius by only about a factor of 2. During inspiral, the inner edge of the disk at first moves inward in coordination with the shrinking binary, but as the orbital evolution accelerates, the rate at which the inner edge moves toward smaller radii falls behind the rate of binary compression. In this stage, the rate of angular momentum transfer from the binary to the disk slows substantially, but the net accretion rate decreases by only 10-20%. When the binary separation is tens of gravitational radii, the rest-mass efficiency of disk radiation is a few percent, suggesting that supermassive binary black holes in galactic nuclei could be very luminous at this stage of their evolution. If the luminosity were optically thin, it would be modulated at a frequency that is a beat between the orbital frequency of the disks surface density maximum and the binary orbital frequency. However, a disk with sufficient surface density to be luminous should also be optically thick; as a result, the periodic modulation may be suppressed.
