Gravity as an emergent phenomenon for spherically symmetric black hole accretion of a multicomponent flow with a relativistic equation of state

We investigate analog gravity phenomena arising as a result of the linear perturbation of the spherically symmetric accretion flows onto nonrotating black holes, where the gravitational field is determined by a set of post-Newtonian pseudo-Schwarzschild black hole potentials and the infalling matter is described by a relativistic multispecies equation of state. The stationary transonic integral accretion solutions corresponding to the steady state of the aforementioned type of accreting systems are constructed and the stability analysis of such solutions is performed through the time-dependent linear perturbation of the accretion flow. Such linear stability analysis leads to the formation of a black hole--like sonic metric embedded within the infalling matter. The acoustic horizons are then identified by constructing the causal structure, i.e., the Carter-Penrose diagrams. The variation of the analog surface gravity corresponding to the aforementioned sonic metric has been studied as a function of various parameters governing the accretion flow.