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The spatially conformally flat approximation (CFA) is a viable method todeduce initial conditions for the subsequent evolution of binary neutron starsemploying the full Einstein equations. Here we review the status of theoriginal formulation of the CFA for the general relativistic hydrodynamicinitial conditions of binary neutron stars. We illustrate the stability of theconformally flat condition on the hydrodynamics by numerically evolving ~100quasi-circular orbits. We illustrate the use of this approximation for orbitingneutron stars in the quasi-circular orbit approximation to demonstrate theequation of state dependence of these initial conditions and how they mightaffect the emergent gravitational wave frequency as the stars approach theinnermost stable circular orbit.

Review of Conformally Flat Approximation for Binary Neutron Star Initial Conditions