ar X iv : g r - qc / 9 81 20 54 v 1 1 6 D ec 1 99 8 A Way to 3 D Numerical Relativity — Coalescing Binary Neutron Stars —

Long baseline interferometers to detect gravitational waves such as TAMA300 [1], GEO600 [2], VIRGO [3], LIGO [4] will be in operation by the end of this century or the beginning of the 21st century. One of the most important sources of gravitational waves for such detectors are coalescing binary neutron stars. PSR1913+16 is the first binary neutron stars found by Hulse and Taylor. The existence of the gravitational waves is confirmed by analyzing the arrival time of radio pulses from PSR1913+16. At present there are three systems like PSR1913+16 for which coalescing time due to the emission of gravitational waves is less than the age of the universe. From these observed systems the event rate of the coalescing binary neutron stars is estimated as 10 ∼ 2× 10 events yr galaxy [5, 6, 7]. From the formation theory of binary neutron stars, the event rate is estimated as 2×10 ∼ 3×10 events yr galaxy [8, 9, 10]. If the event rate is ∼ 2 × 10, two different methods yield the agreement. Since the number density of galaxies is ∼ 10/Mpc, we may expect several coalescing events/year within 200Mpc (∼ 2 × 10events /Mpc). The coalescing binary neutron stars is a possible central engine of cosmological gamma ray bursts. Coalescing binary neutron stars is also a possible site of r-process element production. The eccentricity e and the semimajor axis a of binary neutron stars decrease due to the emission of gravitational waves, and these quantities are related with each other as