  We present the structure of a low angular momentum accretion flows around
rotating compact objects incorporating relativistic corrections up to the
leading post-Newtonian order. To begin with, we formulate the governing
post-Newtonian hydrodynamic equations for the mass and energy-momentum flux
without imposing any symmetries. However, for the sake of simplicity, we
consider the flow to be stationary, axisymmetric, and inviscid. Toward this, we
adapt the polytropic equation of state (EoS) and analyze the vertically
integrated accretion flow confined to the equatorial plane. It is shown that
the spin-orbit effects manifest themselves in the accretion dynamics. In the
present analysis, we focus on global transonic accretion solutions, where a
subsonic flow enters far away from the compact object and gradually gains
radial velocity as it moves inwards. Thus, the flow becomes supersonic after
reaching a certain radius, known as the critical point. To better understand
the transonic solutions and examine the effect of post-Newtonian corrections,
we classify the post-Newtonian equations into semi-relativistic (SR),
semi-Newtonian (SN), and non-relativistic (NR) limits and compare the accretion
solutions and their corresponding flow variables. With these, we find that SR
and SN flow are in good agreement all throughout, although they deviate largely
from the NR ones. Interestingly, the density profile seems to follow the
profile $\rho \propto r^{-3/2}$ in the post-Newtonian regime. The present study
has the potential to connect Newtonian and GR descriptions of accretion
dynamics.
