  For axially symmetric accretion maintained in the hydrostatic equilibrium
along the vertical direction in the Kerr metric, the radial Mach number does
not become unity at the critical point. The sonic points are, thus, formed at a
radial distance different from that where the critical points are formed. We
propose that a modified dynamical sound speed can be defined through the linear
perturbation of the full space-time dependent equations describing the
aforementioned accretion flow structure. The linear stability analysis of such
fluid equations leads to the formation of an wave equation which describes the
propagation of linear acoustic perturbation. The speed of propagation of such
perturbation can be used as the effective sound speed which makes the value of
the Mach number to be unity when evaluated at the critical points. This allows
the critical points to coalesce with the sonic points. We study how the spin
angular momentum of the black hole (the Kerr parameter) influences the value of
the effective sound speed.
