  In this paper we have examined the validity of a proposed definition of
gravitational entropy in the context of accelerating black hole solutions of
the Einstein field equations, which represent the realistic black hole
solutions. We have adopted a phenomenological approach proposed in Rudjord et
al [20] and expanded by Romero et al [21], in which the Weyl curvature
hypothesis is tested against the expressions for the gravitational entropy.
Considering the $C$-metric for the accelerating black holes, we have evaluated
the gravitational entropy and the corresponding entropy density for four
different types of black holes, namely, non-rotating black hole, non-rotating
charged black hole, rotating black hole and rotating charged black hole. We end
up by discussing the merits of such an analysis and the possible reason of
failure in the particular case of rotating charged black hole and comment on
the possible resolution of the problem.
