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The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here we review the status of the original formulation of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasi-circular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasi-circular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect the emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.
We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form,
We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant $Lambda$, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove
Binary neutron stars in circular orbits can be modeled as helically symmetric, i.e., stationary in a rotating frame. This symmetry gives rise to a first integral of the Euler equation, often employed for constructing equilibrium solutions via iterati
The complete class of conformally flat, pure radiation metrics is given, generalising the metric recently given by Wils.
We present results from three-dimensional general relativistic simulations of binary neutron star coalescences and mergers using public codes. We considered equal mass models where the baryon mass of the two Neutron Stars (NS) is $1.4M_{odot}$, descr