On the spin dependence of the emergent gravity phenomena as observed in axially symmetric black hole accretion with spatially varying adiabatic index
The present work addresses an axisymmetrically accreting black hole system from three perspectives: the astrophysical, the dynamical systems, and the emergent gravity standpoint. Steady-state equations governing low angular momentum axially symmetric accretion under a pseudo-Kerr potential are formulated for a multi-species flow with a spatially varying adiabatic index. The resulting transonic solutions are shown to be multi-transonic and may accommodate a stationary shock. Critical points are classified via perturbative dynamical systems methods, and linear stability analysis confirms that the stationary solutions remain stable under radial perturbation. The ensuing acoustic geometry harbours acoustic black holes at the sonic points and an acoustic white hole at the shock location, whose causal structure is constructed via the Carter--Penrose diagram. The surface gravity associated with each acoustic horizon is computed using a generalized expression that accounts for the spatial variation of the local sound speed.