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A modern and largely used approach to obtain Hawking radiation is thetunnelling mechanism. However, in various papers in the literature, theanalysis concerned almost only to obtain the Hawking temperature through acomparison of the probability of emission of an outgoing particle with theBoltzmann factor. In a interesting and well written paper, Banerjee and Majhiimproved the approach, by explicitly finding a black body spectrum associatedwith black holes. On the other hand, this result, which has been obtained byusing a reformulation of the tunnelling mechanism, is in contrast which theremarkable result by Parikh and Wilczek, that, indeed, found a probability ofemission which is compatible with a non-strictly thermal spectrum. By using ourrecent introduction of an effective state for a black hole, here we solve sucha contradiction, through a slight modification of the analysis by Banerjee andMajhi. The final result will be a non-strictly black body spectrum from thetunnelling mechanism. We also show that, for an effective temperature, we canwrite the corresponding effective metric by Hawking's periodicity arguments.Potential important implications for the black hole information puzzle are alsodiscussed

Non-strictly black body spectrum from the tunnelling mechanism