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Spectral and timing properties of accretion flows on a black hole depend ontheir density and temperature distributions, which in turn come from theunderlying dynamics. Thus, an accurate description of the flow which includeshydrodynamics and radiative transfer is a must to interpret the observationalresults. In the case of non-rotating black holes, Pseudo-Newtonian descriptionof surrounding space-time enables one to make a significant progress inpredicting spectral and timing properties. This formalism is lacking forspinning black holes. In this paper, we show that there exists an exact form of'natural' potential derivable from the general relativistic (GR) radialmomentum equation. Use of this potential in an otherwise Newtonian set ofequations allows to describe transonic flows very accurately as is evidenced bycomparing with solutions obtained from the full GR framework. We study theproperties of the critical points and the centrifugal pressure supported shocksin the parameter space spanned by the specific energy and the angular momentum,and compare with the results of GR hydrodynamics. We show that this potentialcan safely be used for the entire range of Kerr parameter $-1<a<1$ for modelingof observational results around spinning black holes. We assume the flow to beinviscid. Thus, it is non-dissipative with constant energy and angularmomentum. These assumptions are valid very close to the black hole as theinfall timescale is much shorter as compared to the viscous timescale.

Transonic accretion and winds around Pseudo-Kerr black holes and comparison with general relativistic solutions