## An Effective Temperature for Black Holes

**Authors:** Christian Corda

The physical interpretation of black hole's quasinormal modes is
fundamental for realizing unitary quantum gravity theory as black holes are
considered theoretical laboratories for testing models of such an ultimate
theory and their quasinormal modes are natural candidates for an
interpretation in terms of quantum levels.
The spectrum of black hole's quasinormal modes can be re-analysed by
introducing a black hole's effective temperature which takes into account
the fact that, as shown by Parikh and Wilczek, the radiation spectrum
cannot be strictly thermal. This issue changes in a fundamental way the
physical understanding of such a spectrum and enables a re-examination
of various results in the literature which realizes important modifies on
quantum physics of black holes. In particular, the formula of the
horizon's area quantization and the number of quanta of area result modified
becoming functions of the quantum "overtone" number n. Consequently,
the famous formula of Bekenstein-Hawking entropy, its sub-leading
corrections and the number of microstates are also modified. Black hole's
entropy results a function of the quantum overtone number too.
We emphasize that this is the first time that black hole's entropy is
directly connected with a quantum number.
Previous results in the literature are re-obtained in the limit n → ∞.

**Comments:** Pages. Journal of High Energy Physics Volume 2011, Number 8, 101

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### Submission history

[v1] 17 May 2011

[v2] 1 Jun 2011

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