  We study the relativistic, time-independent, low angular momentum, inviscid,
advective accretion flow around Kerr black hole. Considering the relativistic
equation of state (REoS), we examine the transonic properties of the flow and
find that there exists an upper bound of the location of the physically
accepted critical point ($r^{\rm max}_{\rm out}$). However, no such limit
exists when an ideal gas equation of state (IEoS) is assumed to describe the
flow. Further, we calculate the global accretion solutions that contain shock
waves and separate the domain of parameter space in angular momentum
($\lambda$) and energy (${\cal E}$) plane. We find ample disagreement between
the shock parameter spaces obtained for REoS and IEoS, respectively. In
general, post-shock flow (equivalently post-shock corona, hereafter PSC) is
characterized by shock location ($r_s$) and compression ratio ($R$, measure of
density compression across the shock front) which are uniquely determined for
flow with given input parameters, namely $({\cal E}, \lambda)$. Using $r_s$ and
$R$, we empirically compute the oscillation frequency ($\nu_{QPO}$) of the
shock front which is in general quasi-periodic (QP) in nature and retrace the
domain of shock parameter space in the $r_s-R$ plane in terms of $\nu_{QPO}$
for REoS around the weakly as well as rapidly rotating black holes. Finally, we
indicate the relevance of the present work to explain the plausible origin of
high frequency QPO (HFQPO) and its connection with the spin ($a_k$) of the
Galactic black hole sources.
