Coalescence of Binary Neutron Stars and Gravitational Radiation

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We have performed numerical simulations for coalescing binary neutron stars using a 3-dimensional general relativistic code and investigate radiation of gravitational waves. A stable code using maximal slicing and pseudo-minimal distortion condition has been obtained, where we found that it is important to calculate the second-derivative of the metric tensor with precision making use of the pseudo-minimal distortion condition. At first, some parts of the gravitational waves are reflected at the numerical boundary, but it is found to be fixed if the grid size is enlarged. We use a 475 × 475 grid in the Cartesian coordinate system. The CPU hours necessary to perform the simulation for each parameter set is approximately 100 hours on Fujitsu VPP5000 with 32 nodes.To evaluate the gravitational radiation, we implemented a gauge-invariant wave extraction and compared the wave forms with a simple estimate of waves from metric perturbation. The energy spectrum of the waves was also evaluated to investigate the possibility that the excitation of the quasi-normal modes of black hole, which may be formed after merger of two stars, can be caught. However, we need more precise calculation with finer grid and larger grid size from various initial data to obtain definite results.The following revision of the code remains for future research; more realistic initial data and other method of gauge-invariant wave extraction. The required CPU hours will be reduced if slightly different coordinate conditions are used.