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We study the relativistic, time-independent, low angular momentum, inviscid,advective accretion flow around Kerr black hole. Considering the relativisticequation of state (REoS), we examine the transonic properties of the flow andfind that there exists an upper bound of the location of the physicallyaccepted critical point ($r^{\rm max}_{\rm out}$). However, no such limitexists when an ideal gas equation of state (IEoS) is assumed to describe theflow. Further, we calculate the global accretion solutions that contain shockwaves and separate the domain of parameter space in angular momentum($\lambda$) and energy (${\cal E}$) plane. We find ample disagreement betweenthe shock parameter spaces obtained for REoS and IEoS, respectively. Ingeneral, post-shock flow (equivalently post-shock corona, hereafter PSC) ischaracterized by shock location ($r_s$) and compression ratio ($R$, measure ofdensity compression across the shock front) which are uniquely determined forflow with given input parameters, namely $({\cal E}, \lambda)$. Using $r_s$ and$R$, we empirically compute the oscillation frequency ($\nu_{QPO}$) of theshock front which is in general quasi-periodic (QP) in nature and retrace thedomain 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, weindicate the relevance of the present work to explain the plausible origin ofhigh frequency QPO (HFQPO) and its connection with the spin ($a_k$) of theGalactic black hole sources.

Low angular momentum relativistic hot accretion flow around Kerr black holes with variable adiabatic index