  In this study, we develop a simplified magnetofluid model in the framework of
GRMHD. We consider an ideal, adiabatic fluid composed of two components, ions
and electrons, having a constant ratio between their temperatures. The flows
are assumed to be governed by gravity, enabling us to employ the ballistic
approximation, treating the streamlines as timelike geodesics. We show that the
model is analytically solvble around a rotating black hole if the angular
velocity of the geodesic $u^\theta$ is vanishing. In the corresponding
solution, which is named the conical solution, we derive a comprehensive set of
explicit expressions for the thermodynamics and the associated magnetic field.
Furthermore, we explore the potential applications of our model to describe the
thick disks and the jets at the horizon scale. Our model provides a direct
pathway for the study of black hole imaging.
