  The generalized uncertainty principle (GUP) is a gravitational correction of
Heisenberg's uncertainty principle, which allows us to probe some features of
quantum gravity even without the full theory. We are used to working with
metric tensors in general relativity; they are convenient to have available
when we wish to calculate physical quantities like Hawking temperature and
black hole shadow. Various authors have tried to incorporate GUP into an
effective metric that allows such calculations. In this note, I point out that
some of these results are not correct due to working with series truncation
rather than the full GUP-corrected expressions. Perhaps more importantly, we
rely too much on heuristic arguments and lack a guiding principle in
constructing the correct effective metric.
