We perform numerical simulations of a three-dimensional (3D) time evolution of pure gravitational waves. We use a conformally flat and K = 0 initial condition for the evolution of the spacetime. We adopt several slicing conditions to check whether a long time integration is possible in those conditions. For the case in which the amplitude of the gravitational waves is low, a long time integration is possible by using the harmonic slice and the maximal slice, while in the geodesic slice ( a = 1) it is not possible. As in the axisymmetric case and also in the 3D case, gravitational waves with a sufficiently high amplitude collapse by their self-gravity and their final fates seem to be as black holes. In this case, the singularity avoidance property of the harmonic slice seems weak, so that it may be inappropriate for the formation problems of the black hole. By means of the gauge-invariant wave extraction technique we compute the waveform of the gravitational waves at an outer region. We find that the nonlinearity of Einstein gravity induces the higher multipole modes even if only a quadrupole mode exists initially.PACS number(s): 04.30.Nk

We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5– requires at least three detectors of sensitivity within a factor of of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

It may be possible to construct a laser interferometer gravitational wave antenna in space with h(rms) approximately 10(-27) at f approximately 0.1 Hz in this century. Using this antenna, (1) typically 10(5) chirp signals of coalescing binary neutron stars per year may be detected with S/N approximately 10(4); (2) we can directly measure the acceleration of the universe by a 10 yr observation of binary neutron stars; and (3) the stochastic gravitational waves of Omega(GW) > or similar to 10(-20) predicted by the inflation may be detected by correlation analysis. Our formula for phase shift due to accelerating motion might be applied for binary sources of LISA.

We estimate a gamma-ray burst (GRB) formation rate based on the new relation between the spectral peak energy (E p ) and the peak luminosity. The new relation is derived by combining the data of E p and the peak luminosities by BeppoSAX and BATSE, and it looks considerably tighter and more reliable than the relations suggested by the previous works. Using the new E p -luminosity relation, we estimate redshifts of the 689 GRBs without known distances in the BATSE catalog and derive a GRB formation rate as a function of the redshift. For the redshift range of 0 z 2, the GRB formation rate increases and is well correlated with the star formation rate, while it keeps constant toward z $ 12. We also discuss the luminosity function and the redshift dependence of the intrinsic luminosity (luminosity evolution).

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