A general relativistic extension to mesh-free methods for hydrodynamics

The detection of gravitational waves has opened a new era for astronomy, allowing for the combined use of gravitational wave and electromagnetic emissions to directly probe the physics of compact objects, still poorly understood. So far, the theoretical modelling of these sources has mainly relied on standard numerical techniques as grid-based methods or smoothed particle hydrodynamics, with only a few recent attempts at using new techniques as moving-mesh schemes. Here, we introduce a general relativistic extension to the mesh-less hydrodynamic schemes in the code GIZMO, which benefits from the use of Riemann solvers and at the same time perfectly conserves angular momentum thanks to a generalised leap-frog integration scheme. We benchmark our implementation against many standard tests for relativistic hydrodynamics, either in one or three dimensions, and also test the ability to preserve the equilibrium solution of a Tolman-Oppenheimer-Volkoff compact star. In all the presented tests, the code performs extremely well, at a level at least comparable to other numerical techniques.