12-129 Christian Corda

Black hole's quantum levels (57K, Latex) Oct 26, 12

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Abstract. By introducing a black hole's eff ective temperature, which takes into account both of the non-strictly thermal and non-strictly continuous characters of Hawking radiation, we recently re-analyzed black hole's quasi-normal modes and interpreted them naturally in terms of quantum levels for emissions of particles. After a careful review of previous results, in this work we improve such an analysis by removing an approximation that we implicitly used in our previous work and by obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its sub-leading corrections and the number of micro-states, i.e. quantities which are fundamental to realize unitary quantum gravity theory, like functions of the quantum overtone number e (emission ) and, in turn, of the black hole's quantum excited level. Another approximation concerning the maximum value of e is also corrected. We also consider quasi-normal modes in terms of quantum levels for absorptions too, in addition to our previous analysis which considered quasi-normal modes naturally associated to Hawking radiation and hence to emissions only. In that case, the above cited quantities result to be functions of the quantum overtone number a (absorption ). In this way, the whole black hole's quantum spectrum, for both of absorption and emission is obtained. Previous results in the literature are re-obtained in the limit of very large overtone numbers e and a and of very small quasi-normal mode's frequency. The results of this paper are very important on the route to realize the underlying unitary quantum gravity theory. In fact, black holes are considered natural theoretical laboratories to test such a theory which has to match the semi-classical results of the present paper.

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