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.
