General relativistic numerical scheme for quasi equilibrium states of irrotational binary neutron star systems

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Our goal in this investigation is to develop a powerful numerical scheme to solve binary neutron star systems in general relativity and to study evolutions of binary neutron star systems. Subsequently we will be able to offer initial models to binary neutron star merging simulations.We need to develop a robust numerical scheme to solve binary neutron star systems in general relativity. We have succeeded in developing a new scheme in which the following two formulations play essential roles. (1) First, the origin of the spherical coordinates are shifted to the lower half region of the original coordinate origin. (2) Second, the bad behavior on the rotational axis of the orbital motion can be eliminate by introducing a new space in which a Laplacian operator in the flat space can be deduced from the nonlinear elliptical operators of the original Einstein equations. In that new space, the Einstein equations are transformed into integral equations by making use of the appropriate Green functions. These two new formulations allow us to get a robust numerical scheme which can give quasiequilibrium solutions of binary neutron stars easily.By applying this new scheme, we have solved structures of binary neutron stars with relatively high stiffness and strong gravity. Evolutionary sequences of binary neutron stars with constant baryon masses show the following results. If we use several realistic equations of state, evolutions will end at the onset of instability, while polytropic stars with soft equations of state would reach contact states without suffering from instability.