Equilibrium configuration of perfect fluid orbiting around black holes in some classes of alternative gravity theories

The hydrodynamic behaviour of perfect fluid orbiting around black holes in spherically symmetric spacetime for various alternative gravity theories has been investigated. For this purpose we have assumed an uniform distribution for the angular momentum density of the rotating perfect fluid. The contours of equipotential surfaces are illustrated in order to obtain the nature of inflow and outflow of matters. It has been noticed that, the marginally stable circular orbits originating from decreasing angular momentum density lead to closed equipotential surfaces along with cusp allowing existence of accretion disks. On the other hand, the growing part of angular momentum density exhibits central rings for which stable configurations are possible. However inflow of matter is prohibited. Among the solutions discussed in this work, the charged $F(R)$ gravity and Einstein-Maxwell-Gauss-Bonnet solution exhibit inflow and outflow of matter with central rings present. These varied accretion disk structure of perfect fluid attribute these spacetimes astrophysical importance. The effect of higher curvature terms predominantly arises from region near the black hole horizon. Hence the structural difference of accretion disk in modified gravity theories with comparison to general relativity may act as an experimental probe for these alternative gravity theories.