We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition .
We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics , and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere ( the apparent horizon ) .
In this paper we focus on irrotational configurations , meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame .
We present results for a binary with polytropic index n = 1 , mass ratio M _ { irr } ^ { BH } / M _ { B } ^ { NS } = 5 and neutron star compaction M _ { ADM, 0 } ^ { NS } / R _ { 0 } = 0.0879 , where M _ { irr } ^ { BH } is the irreducible mass of the black hole , M _ { B } ^ { NS } the neutron star baryon rest-mass , and M _ { ADM, 0 } ^ { NS } and R _ { 0 } the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation , respectively .
Our models represent valid solutions to Einstein ’ s constraint equations and may therefore be employed as initial data for dynamical simulations of black hole-neutron star binaries .