  We investigate the viability of a recently proposed generalization of the
Ashtekar-Olmedo-Singh spacetime for the effective description of the interior
region of a Schwarzschild black hole within the framework of loop quantum
cosmology. The approach is based on a choice of polymerization parameters that
is more general than the ones previously considered in the literature and that
results in the natural appearance of two times to describe the solutions. If
one is interested in examining the physics derived from this model, it is
fundamental to ensure that one can attain a well-defined effective geometry in
the whole region under consideration, in particular as regards the redundancy
of the two times, which one needs to express in terms of a single time
coordinate. In order to determine whether this requirement is met, we analyze
the definition of these times and their relation. We show that one can reach an
acceptable interior spacetime geometry by exploiting the freedom to define the
origins of the two times independently.
