GRAVITATIONAL-RADIATION FROM COALESCING BINARY NEUTRON-STARS .5. POST-NEWTONIAN CALCULATION

We present the results of three dimensional post-Newtonian calculation of coalescing binary neutron stars including gravitational radiation reaction. We use the finite different method (FDM) and the hydrodynamics equations are integrated using van Leer's scheme with the total variation diminishing (TVD) condition. The calculation is started from a binary system consisting of two simple spherical polytropes with gamma = 2. We per-form also a calculation from the same initial condition but neglecting the post-Newtonian terms and compare it with the post-Newtonian calculation in order to estimate effects of general relativity. We find that shock wave is induced by the first centrifugal bounce in the post-Newtonian calculation while it is not in the Newtonian one. It is because general relativity effectively increases the gravitational force. The shock wave makes the matter reexpand and the contraction-expansion oscillation lasts longer in the post-Newtonian case. As a result the total energy of the gravitational radiation increases. Although the evolution of the density distribution looks so different, the general relativistic effect on the waveform is small.