Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum

Details Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum

2009-10-15

arxiv.org/abs/0910.2755v1

Physics

General Physics

15 pages

Scientific paper

Firstly, we propose a new area spectrum based on the Einstein-Kaufman pseudo tensor by pointing out an error in the previous derivation of the area spectrum based on Ashtekar's variable; instead of the norm of Ashtekar's gravitational electric field, we show that the norm of our "new" gravitational electric field based on this pseudo tensor gives the correct area spectrum. Remarkably, by using this new area spectrum, we "almost correctly" predict the Bekenstein-Hawking area entropy relation without adjusting Immirzi parameter; we get $0.997...$ for a formula which, when naively calculated, should come out to be 1 if the black hole entropy is $A/4$. We conjecture that this difference 0.003 is due to the extra dimensions which modify the area spectrum; this difference gives a very strong constraint on the size of the extra dimensions which should be understood by future research. Secondly, we show that the degeneracy of black hole state should be $\sqrt{A}(e^{A/4}-1)$ rather than simply $e^{A/4}$, if the Hawking radiation agrees with the Planck law. By calculating this degeneracy numerically using our new area spectrum, we show that this is the case except for the case when $A$ is small. Also, by the same numerical calculations, we show that the area spectrum predicted by Ashtekar's variable theory doesn't satisfy our degeneracy $\sqrt{A}(e^{A/4}-1)$. As our radiation spectrum deviates from the Planck law for the small frequency of photon, our area spectrum can be either falsified or verified if the Hawking radiation, with its spectrum, is observed at LHC.

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