Perfect relativistic magnetohydrodynamics around black holes in horizon penetrating coordinates

Plasma accreting processes on black holes represent a central problem for relativistic astrophysics. Inthis context, here we specifically revisit the classical Ruffini-Wilson work developed for analyticallymodeling via geodesic equations the accretion of perfect magnetized plasma on a rotating Kerr black hole.Introducing the horizon penetrating coordinates found by Doran 25 years later, we revisit the entireapproach studying Maxwell invariants, electric and magnetic fields, volumetric charge density andelectromagnetic total energy. We finally discuss the physical implications of this analysis.