A new analytical model of magnetofluids surrounding rotating black holes

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.