Multi-criticality and related bifurcation in accretion discs around non-rotating black holes -- an analytical study

Abstract

Low angular momentum, general relativistic, axially symmetric accretion of hydrodynamic fluid onto Schwarzschild black holes may undergo more than one critical transition. To obtain the stationary integral solutions corresponding to such multicritical accretion flow, one needs to employ numerical solutions of the corresponding fluid dynamics equations. In the present work, we develop a completely analytical solution scheme which may be used to find several trans-critical flow behaviours of aforementioned accretion, without explicitly solving the flow equations numerically.We study all possible geometric configurations of the flow profile, governed by all possible thermodynamic equations of state. We use Sturm's chain algorithm to find out