Relativistic numerical model for close neutron-star binaries

We describe a numerical method for calculating the (3+1)-dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial three-metric chosen to be conformally flat. Against this solution to the general relativistic field equations, the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole ($l=4\mathrm{}$) order including both mass and current moments and a correction for the slow-motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution. In the present work we illustrate the method by applying this model to evaluate various orbits of two neutron stars with a gravitational mass of $1.45M_{\odot }$ near the time of the final merger. We discuss the evidence that, for a realistic neutron-star equation of state, general relativistic effects may cause the stars to individually collapse into black holes prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated.