Workshop From geometry to numerics
IHP, Paris, 20-24 November 2006

Koji Uryu (Univ. Wisconsin-Milwaukee, USA)

Equilibrium binary neutron star data in circular orbits

Equilibria of binary neutron stars data in close circular orbits are numerically computed using two formulations; the waveless formulation to general relativity, and the hybrid formulation which is helically symmetric in the near zone and waveless outside.  The new formulations exactly solve the Einstein-Euler system written in 3+1 form on a spacelike hypersurface.  In the waveless formulation, all components of the field equation are written elliptic equations, and all metric components, including the spatial metric, have Coulomb-type fall off.  Our waveless condition is to choose the time derivative of conformal three-metric to vanish on a spacelike hypersurface and impose stationarity in rotating frame on the other time derivative terms.  Two independent numerical codes, one based on a finite difference method, the other on a spectral method, are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are successfully computed.  The binding energy of the system near its final orbit deviates from earlier results of third post-Newtonian and of spatially conformally flat calculations.  The new solutions may serve as initial data for merger simulations and as members of quasiequilibrium sequences to generate gravitational wave templates, and may improve estimates of the gravitational-wave cutoff frequency set by the last inspiral orbit.

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