We present new sequences of general relativistic , quasiequilibrium black hole-neutron star binaries .
We solve for the gravitational field in the conformal thin-sandwich decomposition of Einstein ’ s field equations , coupled to the equations of relativistic hydrostatic equilibrium for a perfect fluid .
We account for the black hole by solving these equations in the background metric of a Schwarzschild black hole whose mass is much larger than that of the neutron star .
The background metric is treated in Kerr-Schild as well as isotropic coordinates .
For the neutron star , we assume a polytropic equation of state with adiabatic index \Gamma = 2 , and solve for both irrotational and corotational configurations .
By comparing the results of irrotational and synchronized configurations with the same background metric , we conclude that the effect of the rotation on the location of tidal break-up is only on the order of a few percent .
The different choices in the background also lead to differences of order a few percent , which may be an indication of the level to which these configurations approximate quasiequilibrium .