  We derive the equation governing the axial-perturbations in the space-time of
a non-rotating uncharged primordial black hole (PBH), produced in early
Universe, whose metric is taken as the generalized McVittie metric. The
generalized McVittie metric is a cosmological black hole metric, proposed by V.
Faraoni and A. Jacques in 2007 [Phys. Rev. D 76, 063510 (2007)]. This describes
the space-time of a Schwarzschild black hole embedded in FLRW-Universe, while
allowing its mass-change. Our derivation has basic similarities with the
procedure of derivation of S. Chandrasekhar, for deriving the Regge-Wheeler
equation for Schwarzschild metric [S. Chandrasekhar, The Mathematical Theory of
Black holes ; Oxford University Press (1983)] ; but it has some distinct
differences with that due to the complexity and time-dependency of the
generalized McVittie metric. We show that after applying some approximations
which are very well valid in the early radiation-dominated Universe, the
overall equation governing the axial perturbations can be separated into radial
and angular parts, among which the radial part is the intended one, as the
angular part is identical to the case of Schwarzschild metric as expected. We
identify the potential from the Schr\"odinger-like format of the equation and
draw some physical interpretation from it.
