NS-NS merger simulations address a broad set of questions, which can be roughly summarized as follows (note the same questions apply to BH-NS mergers as well):
The influence of the gravitational formalism used in a numerical simulation on the answer one finds for the questions above differs item by item. Determining the final fate of a merging system is highly dependent on the gravitational formalism; NS-NS merger remnants only undergo collapse in quasi-relativistic and fully GR schemes. Moreover, orbital dynamics at separations comparable to the ISCO and even somewhat larger depend strongly on the gravitational scheme. In particular, mass loss rates into a disk are often suppressed by orders of magnitude in GR calculations when compared to CF simulations, and even more so in comparison to PN and Newtonian calculations. EM emission profiles from a disk are difficult to calculate accurately without the use of full GR for this reason. On the other hand, while GR is required to calculate the exact GW signal from a merger, even early Newtonian simulations predicted many of the qualitative GW emission features correctly, and PN and CF schemes yielded results with some degree of quantitative accuracy about the full wavetrain. B-fields have only begun to be explored, but it already seems clear that they will affect the hydrodynamical evolution primarily after the merger in cases where differential rotation in a HMNS or disk winds up magnetic field strengths up to energy equipartition levels, vastly stronger than those found in pre-merger NSs. For such configurations, non-relativistic calculations can often reproduce the basic physical scenario but full GR is required to properly understand the underlying dynamics. Finally, the production of r-process elements, which depends sensitively on the thermodynamic evolution of the merger, seems to generally disfavor binary mergers as a significant source of the observed stellar abundances since the temperature and thus the electron fraction of the fluid remains too small , regardless of the nature of the gravitational treatment used in the calculations. This picture may need to be revised if significant mass loss occurs from the hot accretion disk that forms around the central post-merger object, possibly due to energy release from the r-process itself, but numerical calculations do not currently predict sufficient mass loss to match observations . We will address each of these topics in greater detail in the sections below.
Since the first NS-NS merger calculations, there have been two main directions for improvements: more accurate relativistic gravitation, resulting in the current codes that operate using a self-consistent fully GR approach, and the addition of microphysical effects, which now include treatments of magnetic fields and neutrino/EM radiation. Noting that several of the following developments overlapped in time, e.g., the first full GR simulations by Shibata and Uryū  are coincident with the first PN SPH calculations, and predate the first CF SPH calculations, we consider in turn the original Newtonian calculations, those performed using approximate relativistic schemes, the calculations performed using full GR, and finally those that have included more advanced microphysical treatments.
Living Rev. Relativity 15, (2012), 8
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