 12129 Christian Corda
 Black hole's quantum levels
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Oct 26, 12

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Abstract. By introducing a black hole's eff ective temperature,
which takes into account both of the nonstrictly thermal and nonstrictly continuous characters of Hawking radiation, we recently reanalyzed black hole's quasinormal 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 BekensteinHawking entropy, its subleading corrections and the number of microstates, 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 quasinormal modes in terms of quantum levels for
absorptions too, in addition to our previous analysis which considered
quasinormal 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 reobtained in the limit of very large overtone numbers e
and a and of very small quasinormal 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 semiclassical results of the present paper.
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