  General relativistic, axisymmetric flow of low angular momentum accretion
around a Kerr black hole can have certain geometric configuration where the
flow is maintained in hydrostatic equilibrium along the vertical direction
(direction orthogonal to the equatorial plane of the flow). The flow thickness
for such accretion models becomes a function of the local radial distance
measured from the black hole horizon. There are three types of functions
defined in the literature which resemble the thickness of the flow for such a
configuration. We formulate the equations governing the steady state
astrophysical accretion characterized by both the polytropic as well as the
isothermal equation of state in classical thermodynamics. We solve the
equations within the framework of such geometric configuration for three
different thickness functions, to obtain the multi-transonic, shocked,
stationary integral accretion solutions. Such solutions enable us to study how
flow thickness influences the dependence of the properties of post-shock flows
on black hole spin angular momentum, i.e., the Kerr parameter. For
temperature-preserving standings shocks, we find that the post-shock part of
the disc can become luminous and considerable amount of gravitational energy
carried by the accreting fluid can get liberated at the shock. We find which
kind of thickness function produces the maximum liberated energy, making the
disc most luminous.
