A general relativistic magnetohydrodynamics extension to mesh-less schemes in the code GIZMO

The profound comprehension of the evolution and phenomenology of an Active Galactic Nucleus requires an accurate exploration of the dynamics of the magnetized gaseous disk surrounding the massive black hole in the centre. Many numerical simulations have studied this environment using elaborate grid-based codes, but in recent years, new mesh-less schemes have exhibited excellent conservation properties and good accuracy at a more moderate computational cost. Still, none implement general relativistic magnetic fields, a fundamental ingredient to model an accretion disk around a massive black hole. We present here a general relativistic magnetohydrodynamics (GRMHD) scheme working within the mesh-less framework of the code \texttt{GIZMO}. We implement the hyperbolic divergence cleaning procedure, consistently extended to general relativistic effects, to keep the magnetic field divergence under safe levels. We benchmark the scheme against various relativistic magnetohydrodynamics stress tests, considering different dimensionalities and both a Minkowski or a Schwarzchild/Kerr background. To date, this is the first GRMHD scheme working in a mesh-free environment.