1212.0746 (Christian Corda)

Quantum transitions of minimum energy for Hawking quanta in highly
excited black holes    [PDF]

Christian Corda

By adding an hypothesis of the locality of particle emission in a black hole, Yoon recently argued that, differently from previous literature, in loop quantum gravity the Hawking radiation spectrum is discrete even in the case that the allowed area is not simply the integer multiples of a single unit area. This looks consistent with our observation that the non-strictly thermal character of Hawking radiation implies that the spectrum is also not strictly continuous. Yoon also found that the Hawking radiation spectrum is truncated below a certain frequency, given a certain Hawking temperature of the black hole T_{H}, corresponding to a minimum energy of an emitted particle E_{min}\approx\alpha T_{H} where alpha is a constant which depends on the considered scenario (isolated horizon scenario, Tanaka-Tamaki scenario Kong-Yoon scenario). We match these results with our recent result that permits to find the frequency of emission for highly excited black hole's transitions between different levels if one interprets black hole's quasi normal modes naturally in terms of quantum levels for emissions of Hawking quanta. The analysis permits to find that the minimum energies found by Yoon should always correspond to imaginary Hawking temperatures (and imaginary correspondent masses) in our approach. Hence, the analysis in this work implies that the results by Yoon, which arise from loop quantum gravity, are not consistent with our semi-classical results for highly excited black holes. Maybe that the results by Yoon can be correct for for non-highly excited black holes, but, in any case, our analysis renders further problematical the match between loop quantum gravity and semi-classical theory.

View original: http://arxiv.org/abs/1212.0746