Thursday, December 15, 2011

Spectroscopy of a black hole and its horizon entropy

The idea of Isolated and Dynamical Horizon theory was first worked out by Heyward in 1994. He derived the complete definition of a marginally null surface that is trapped on a black hole horizon.

A few years later Ashtekar and his colleagues re-wrote the same theory in the language of Ashtekar- Sen variables. Before this development Rovelli has argued that a black hole entropy should be proportional with its horizon area. Lee Smolin linked loop quantum gravity to topological field theory and argued that a black hole should be described by a Chern Simon’s action.

Later on, Krasnov based on all the above mentioned ideas argued the derivation of a black hole entropy from the counting of puncture states. A ‘sequence’ of punctures on a horizon explains the wave function of the horizon. Being a sequence, the punctures are ordered and this make them distinguishable. However, there is no physical evidence why should one restricts the wave functions into a sequence and not a set of punctures in which there is no generic order, thus no distinguishability.

Given this in the quantum horizon theory, I noticed an internal degeneracy in the nature of area operator. Since the area eigenstates are insensitive to the completely tangential edges residing on the horizon, the edges describing a quantum surface carries a local distinguishability. The complete spectrum of area provides the Bekenstein-Hawking entropy, which using Olaf Dreyer’s conjecture it becomes consistent with the evaporation of minimal area cell with the corresponding area of the highly damping quanta.

This proposes a kinematical picture for defining a quantum horizon via spin foam models, however the dynamics of such a model has not yet initiated to be studied. . A new value was devoted to the Immirzi parameter. Considering the full spectrum of area and using the semi-classical conjecture that on a black hole the horizon area and the hole energy are proportional

I noticed a strong amplification in some selected frequencies radiated away from a black hole due to its horizon fluctuations. The full spectrum of a black hole radiation was extracted and the bright lines in the spectrum turn out to be unblended and narrow enough to become observable.
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