  We analyze changes of the Immirzi parameter in loop quantum gravity and
compare their consequences with those of Lorentz boosts and constant conformal
transformations in black hole physics. We show that the effective value deduced
for the Planck length in local measurements of vacuum black holes by an
asymptotic observer may depend on its conformal or Lorentz frame. This
introduces an apparent ambiguity in the expression of the black hole entropy
which is analogous to that produced by the Immirzi parameter. For quantities
involving a notion of energy, the similarity between the implications of the
Immirzi ambiguity and a conformal scaling disappears, but the parallelism with
boosts is maintained.
