  This work focuses on some key aspects of the General Relativistic
(GR)-magnetohydrodynamic (MHD) applications in High-Energy Astrophysics. We
discuss the relevance of the GR-HD counterparts formulation exploring the
geometrically thick disk models and constraints of the GR-MHD shaping the
physics of accreting configurations. Models of clusters of tori orbiting a
central super-massive black hole (SMBH) are described. These orbiting tori
aggregates form sets of geometrically thick, pressure supported, perfect fluid
tori, associated to complex instability processes including tori collision
emergence and empowering a wide range of activities related expectantly to the
embedding matter environment of Active Galaxy Nuclei. Some notes are included
on aggregates combined with proto-jets, represented by open cusped solutions
associated to the geometrically thick tori. This exploration of some key
concepts of the GR-MHD formulation in its applications to High-Energy
Astrophysics starts with the discussion of the initial data problem for a most
general Einstein-Euler-Maxwell system addressing the problem with a
relativistic geometric background. The system is then set in quasi linear
hyperbolic form, and the reduction procedure is argumented. Then,
considerations follow on the analysis of the stability problem for
self-gravitating systems with determined symmetries considering the
perturbations also of the geometry part on the quasi linear hyperbolic onset.
Thus we focus on the ideal GR-MHD and self-gravitating plasma ball. We conclude
with the models of geometrically thick GR-HD disks gravitating around a Kerr
SMBH in their GR-HD formulation and including in the force balance equation of
the disks the influence of a toroidal magnetic field, determining its impact in
tori topology and stability
