Effect of matter geometry on low angular momentum black hole accretion in the Kerr metric

This work illustrates how the formation of energy-preserving shocks for polytropic accretion and temperature-preserving shocks for isothermal accretion are influenced by various geometrical configurations of general relativistic, axisymmetric, low-angular-momentum flow in the Kerr metric. Relevant pre- and post-shock states of the accreting fluid, both dynamical and thermodynamic, have been studied comprehensively. Self-gravitational back-reaction on the metric has not been considered in the present context. An elegant eigenvalue-based analytical method has been introduced to provide qualitative descriptions of the phase-orbits corresponding to stationary transonic accretion solutions, without resorting to involved numerical schemes. Effort has been made to understand how the weakly-rotating flow behaves in close proximity of the event horizon and how such `quasi-terminal' quantities are influenced by the black hole spin for different matter geometries. Our main purpose is thus to mathematically demonstrate that for non-self-gravitating accretion, separate matter geometries, in addition to the corresponding space-time geometry, control various shock-induced phenomena observed within black hole accretion discs. This work is expected to reveal how such phenomena observed near the horizon depend on physical environment of the source harbouring a supermassive black hole at its centre. It is also expected to unfold correspondences between the dependence of accretion-related parameters on flow geometries and on black hole spin. Temperature-preserving shocks in isothermal accretion may appear bright as substantial amount of rest-mass energy of the infalling matter gets dissipated at the shock surface, and the prompt removal of such energy to maintain isothermality may power the X-ray/IR flares emitted from our Galactic centre.