  A number of `modified' Newtonian potentials of various forms are available in
the literature which accurately approximate some general relativistic effects
important for studying accretion discs around a Schwarzschild black hole. Such
potentials may be called `pseudo-Schwarzschild' potentials because they nicely
mimic the space-time around a non-rotating/slowly rotating compact object. In
this paper, we examine the validity of the application of some of these
potentials to study the spherically symmetric, transonic, hydrodynamic
accretion onto a Schwarzschild black hole. By comparing the values of various
dynamical and thermodynamic accretion parameters obtained for flows using these
potentials with full general relativistic calculations, we have shown that
though the potentials discussed in this paper were originally proposed to mimic
the relativistic effects manifested in disc accretion, it is quite reasonable
to use most of the potentials in studying various dynamical as well as
thermodynamic quantities for spherical accretion to compromise between the ease
of handling of a Newtonian description of gravity and the realistic situations
described by complicated general relativistic calculations. Also we have shown
that depending on the chosen regions of parameter space spanned by specific
energy ${\cal E}$ and adiabatic index $\gamma$ of the flow, one potential may
have more importance than another and we could identify which potential is the
best approximation for full general relativistic flow in Scwarzschild
space-time for particular values of ${\cal E}$ and $\gamma$.
