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Numerical relativity simulations are essential to study the last stages ofthe binary neutron star coalescence. Unfortunately, for stable simulationsthere is the need to add an artificial low-density atmosphere. Here we discussa new framework in which we can effectively set the density surrounding theneutron stars to zero to ensure a more accurate simulation. We test our methodwith a number of single star test cases and for an equal mass binary neutronstar simulation. While the bulk motion of the system is not influenced, andhence, there is no improvement with respect to the emitted gravitational-wavesignal, we find that the new approach is superior with respect to massconservation and it allows a much better tracking of outward moving material.This will allow a more accurate simulation of the ejected material and supportsthe interpretation of present and future multi-messenger observations with moreaccurate numerical relativity simulations.

Increasing the Accuracy of Binary Neutron Star Simulations with an improved Vacuum Treatment