Edited by Ray d'Inverno
Publisher: Cambridge University Press
Print Publication Year: 1992
Online Publication Date:December 2009
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511524639.018
Abstract. We present three-dimensional Newtonian and post-Newtonian codes, including the gravitational radiation damping effect, using a finite difference method. We follow the emission of gravitational radiation using the quadrupole approximation. Using these codes we calculate the coalescence of a neutron star binary. For Newtonian calculations the initial configuration is given as a hydrostatic equilibrium model of a close neutron-star binary. Calculations were performed for neutron stars of different masses as well as of the same masses. In order to evaluate general relativistic effects, we compare the results of the calculation of the coalescence of a binary comprising two spherical neutron stars using the post-Newtonian code with results using the Newtonian code.
The most promising sources for laser-interferometric gravitational-wave detectors are catastrophic events such as the gravitational collapse of a star or the coalescence of a black-hole or neutron-star binary. We need to know the characteristics of the waves for design of detectors. It requires general relativistic calculations of stellar collapse and binary coalescence. In the last decade, 2 dimensional (2D) calculations were successfully performed for a head-on collision of two black holes (Smarr 1979) and axisymmetric collapse of a rotating star (Stark and Piran 1986). They found that the efficiency of gravitational wave emission (the ratio of the energy emitted in gravitational radiation to the total rest mass) is less than 0.1%. Nakamura, Oohara and Kojima (1987), on the other hand, pointed out that the efficiency may be much greater in non-axisymmetric black-hole collision.