We study the relativistic accretion flow in a generic stationary axisymmetric space-time and obtain an effective potential ( \Phi ^ { eff } ) that accurately mimics the general relativistic features of Kerr black hole having spin 0 \leq a _ { k } < 1 .
Considering the accretion disc to be confined around the equatorial plane of a rotating black hole and using the relativistic equation of state , we examine the properties of the relativistic accretion flow and compare it with the same obtained form semi-relativistic as well as non-relativistic accretion flows .
Towards this , we first investigate the transonic properties of the accretion flow around the rotating black hole where good agreement is observed for relativistic and semi-relativistic flows .
Further , we study the non-linearities such as shock waves in accretion flow .
Here also we find that the shock properties are in agreement for both relativistic and semi-relativistic flows irrespective of the black hole spin ( a _ { k } ) , although it deviates significantly for non-relativistic flow .
In fact , when the particular shocked solutions are compared for flows with identical outer boundary conditions , the positions of shock transition in relativistic and semi-relativistic flows agree well with deviation of 6 - 12 \% for 0 \leq a _ { k } \leq 0.99 , but vast disagreement is observed for non-relativistic flow .
In addition , we compare the parameter space ( in energy ( { \cal E } ) and angular momentum ( \lambda ) plane ) for shock to establish the fact that relativistic as well as semi-relativistic accretion flow dynamics do show close agreement irrespective of a _ { k } values , whereas non-relativistic flow fails to do so .
With these findings , we point out that semi-relativistic flow including \Phi ^ { eff } satisfactorily mimics the relativistic accretion flows around Kerr black hole .
Finally , we discuss the possible implications of this work in the context of dissipative advective accretion flow around Kerr black holes .