Non-strictly black body spectrum from the tunnelling mechanism

The tunnelling mechanism is widely used to explain Hawking radiation. However, in many cases the analysis used to obtain the Hawking temperature only involves comparing the emission probability for an outgoing particle with the Boltzmann factor. Banerjee and Majhi improved this approach by explicitly finding a black body spectrum associated with black holes. Their result, obtained using a reformulation of the tunnelling mechanism, is in contrast to that of Parikh and Wilczek, who found an emission probability that is compatible with a non-strictly thermal spectrum. Using the recently identified effective state for a black hole, we solve this contradiction via a slight modification of the analysis by Banerjee and Majhi. The final result is a non-strictly black body spectrum from the tunnelling mechanism. We also show that for an effective temperature, we can express the corresponding effective metric using Hawking's periodicity arguments. Potential important implications for the black hole information puzzle are discussed.