Non-strictly black body spectrum from the tunnelling mechanism
  A modern and largely used approach to obtain Hawking radiation is the
tunnelling mechanism. However, in various papers in the literature, the
analysis concerned almost only to obtain the Hawking temperature through a
comparison of the probability of emission of an outgoing particle with the
Boltzmann factor. In a interesting and well written paper, Banerjee and Majhi
improved the approach, by explicitly finding a black body spectrum associated
with black holes. On the other hand, this result, which has been obtained by
using a reformulation of the tunnelling mechanism, is in contrast which the
remarkable result by Parikh and Wilczek, that, indeed, found a probability of
emission which is compatible with a non-strictly thermal spectrum. By using our
recent introduction of an effective state for a black hole, here we solve such
a contradiction, through a slight modification of the analysis by Banerjee and
Majhi. The final result will be a non-strictly black body spectrum from the
tunnelling mechanism. We also show that, for an effective temperature, we can
write the corresponding effective metric by Hawking's periodicity arguments.
Potential important implications for the black hole information puzzle are also
discussed
