Influence of geometrical configuration on low angular momentum relativistic accretion around rotating black holes

We illustrate 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 postshock states of the accreting fluid, both dynamical and thermodynamic, are studied comprehensively. Self-gravitational backreaction on the metric is not considered in the present context. An elegant eigenvalue-based analytical method is introduced to provide qualitative descriptions of the phase orbits corresponding to stationary transonic accretion solutions without resorting to involved numerical schemes. Effort is made to understand how the weakly rotating flow behaves in close proximity to the event horizon and how such "quasiterminal" 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 disks. We expect to reveal how such phenomena observed near the horizon depend on the physical environment of the source harboring a supermassive black hole at its center. We also expect 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 a 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 Center.