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.

Recent studies suggest that binary neutron star (NS-NS) mergers robustly produce the heavy rprocess nuclei above the atomic mass number A ∼ 130 because of their ejecta consisting of almost pure neutrons (electron fraction of Y e < 0.1). However, little production of the lighter r-process nuclei (A ≈ 90-120) conflicts with the spectroscopic results of r-process-enhanced Galactic halo stars. We present, for the first time, the result of nucleosynthesis calculations based on the fully generalrelativistic simulation of a NS-NS merger with approximate neutrino transport. It is found that the bulk of the dynamical ejecta are appreciably shock-heated and neutrino-processed, resulting in a wide range of Y e (≈ 0.09-0.45). The mass-averaged abundance distribution of calculated nucleosynthesis yields is in reasonable agreement with the full-mass range (A ≈ 90-240) of the solar r-process curve. This implies, if our model is representative of such events, that the dynamical ejecta of NS-NS mergers can be the origin of the Galactic r-process nuclei. Our result also shows that the radioactive heating after ∼ 1 day from the merging, giving rise to r-process-powered transient emission, is dominated by the β-decays of several species close to stability with precisely measured half-lives. This implies that the total radioactive heating rate for such an event can be well constrained within about a factor of two if the ejected material has a solar-like r-process pattern.

Numerical-relativity simulations for the merger of binary neutron stars are performed for a variety of equations of state (EOSs) and for a plausible range of the neutron-star mass, focusing primarily on the properties of the material ejected from the system. We find that a fraction of the material is ejected as a mildly relativistic and mildly anisotropic outflow with the typical and maximum velocities ∼ 0.15 -0.25c and ∼ 0.5 -0.8c (where c is the speed of light), respectively, and that the total ejected rest mass is in a wide range 10 −4 -10 −2 M , which depends strongly on the EOS, the total mass, and the mass ratio. The total kinetic energy ejected is also in a wide range between 10 49 and 10 51 ergs. The numerical results suggest that for a binary of canonical total mass 2.7M , the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the r-process [1][2][3] or through the formation of blast waves during the interaction with the interstellar matter [4], if the EOS and mass of the binary are favorable ones.