  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.
