  For low angular momentum axially symmetric accretion flow maintained in
hydrostatic equilibrium along the vertical direction, the value of the Mach
number at the critical points deviates from unity, resulting in the
non-isomorphism of the critical and the sonic points. This introduces several
undesirable complexities while analytically dealing with the stationary
integral accretion solutions and the corresponding phase portraits. We propose
that introduction of an effective dynamical sound speed may resolve the issue
in an elegant way. We linear perturb the full spacetime-dependent general
relativistic Euler and the continuity equations governing the structure and the
dynamics of accretion disc in vertical equilibrium around Schwarzschild black
holes and identify the sonic metric embedded within the stationary background
flow. Such metric describes the propagation of the linear acoustic perturbation
inside the accretion flow. We construct the wave equation corresponding to that
acoustic perturbation and find the speed of propagation of such perturbation.
We finally show that the ordinary thermodynamic sound speed should be
substituted by the speed of propagation of the linear acoustic wave which has
been obtained through the dynamical perturbation. Such substitution will make
the value of Mach number at the critical point to be equal to unity. Use of the
aforementioned effective sound speed will lead to a modified stationary disc
structure where the critical and the sonic points will be identical.
