1814-2014 : 200 years of spectroscopy / 200 ans de spectroscopie

From the Fraunhofer spectral lines of Sun light... / Du spectre de raies solaires de Fraunhöfer 

[In 1814 Joseph von Fraunhofer invented the spectroscope,] looking for ways to check (and improve) the quality of telescopes he was making. He rediscovered the dark lines in the sun's spectrum while measuring the dispersive powers of various kinds of glass for light of different colors. As he worked on this project, he noticed that a bright 'orange' line (due to sodium, but he didn't know that) in the spectrum of the flame he was using was in the same position as the dark D-line (see below). This same line had been observed in flames from alcohol and sulfur as well as from candles. Fraunhofer mapped out the 574 thin black lines that he observed in the sun's spectrum. Eight of the most prominent lines were labeled A to G. Today, these lines are known as the Fraunhofer lines

... to the Bekenstein-Mukhanov discrete spectrum of  Black Holes Hawking radiation? ... au spectre de Bekenstein-Mukhanov discret pour le rayonnement de Hawking des trous noirs

[The area quantization of 2d manifolds] can have far-reaching consequences for black holes and de Sitter space. In particular, the area of the black hole horizon must be quantized in integers of the Planck area (see also [8]). Because the area of a black hole of mass M is equal to 
A = 16πM2, 
this implies mass quantization
Mn = √n / 2 
As it was shown in [9] Hawking radiation in this case can be considered as a result of quantum transitions from the level n to the nearby levels n−1,n−2,... As a result even for large black holes Hawking radiation is emitted in discrete lines and the spectrum with the thermal envelope is not continuous. The distance between the nearby lines for large black holes is of order
ω = Mn −Mn-1 ≃ 1 / 4√n =1 / 8M 
and proportional to Hawking temperature, while the width of the line is expected to be at least ten times less than the distance between the lines [9]. Note that taking the minimal area to be α larger than the Planck area changes the distance between the lines by a factor α2. Thus area quantization can be experimentally verified if evaporating black hole will be discovered.
(last revised 9 Sep 2014 (this version, v2))

We develop the idea that, in quantum gravity where the horizon fluctuates, a black hole should have a discrete mass spectrum with concomitant line emission. Simple arguments fix the spacing of the lines, which should be broad but unblended. Assuming uniformity of the matrix elements for quantum transitions between near levels, we work out the probabilities for the emission of a specified series of quanta and the intensities of the spectral lines. The thermal character of the radiation is entirely due to the degeneracy of the levels, the same degeneracy that becomes manifest as black hole entropy. One prediction is that there should be no lines with wavelength of order the black hole size or larger. This makes it possible to test quantum gravity with black holes well above Planck scale.

(Submitted on 10 May 1995)

A spectral dream : quantum gravitation phenomenology  

last revised 8 Dec 2011 (this version, v2)


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