Discrete area spectrum and the Hawking radiation spectrum
Blackbody radiation is a phenomenon whereby every object emits light due to its heat. For example, the Sun emits light, the wavelength of which is visible to our eyes. Another example of objects that emit blackbody radiation would be human beings, which emit infrared rays, a type of light that is not visible to our eyes; however, these infrared rays are visible using an infrared camera, or a device such as night-vision goggles.
A natural question that one may ask is, why is the light emitted by the Sun visible to our eyes, while the light emitted by human beings not visible to our eyes?
It is because the Sun is much hotter than the human beings, so the Sun emits light with shorter wavelengths and higher energies. In fact, it is known that the wavelength of light that an object radiates by blackbody radiation depends only on the object’s temperature. To be more precise, an object emits all kinds of light - that is, light of all wavelengths - by blackbody radiation, but it emits the light with certain wavelengths more than the light with other wavelengths. The relative proportions of these different kinds of emitted light depend only on the temperature of the object.
In 1900, Max Planck came up with the mathematical derivation of the amount of these different kinds of emitted light present in blackbody radiation, for which he later received a Nobel Prize. Because of this work, he is known as the “father” of quantum physics.
In 1974, Stephen Hawking mathematically showed that a black hole has a temperature and emits light with certain wavelengths, the distribution of which is exactly given by the Planck’s formula for the blackbody radiation at that black hole’s given temperature. However, Stephen Hawking’s derivation was only semi-classical. By semi-classical, I mean half classical and half quantum. Since our universe is described by quantum mechanics and his derivation is not fully quantum, it is only an approximation,.
In 1995, Bekenstein and Mukhanov showed that the light emitted by the Hawking radiation allows only discrete value of the wavelength if the area spectrum is discrete. In other words, in usual blackbody radiation case, light of every wavelength is emitted even though certain wavelengths are emitted more than others. Bekenstein and Mukhanov argued in this paper that only light with certain discrete wavelength values is emitted.
Let me explain the reason behind this discreteness of wavelength. When a black hole radiates light, its area is decreased. We know that there are certain allowed values for the amount of decrease in area, since area is quantized as I explained in earlier articles. As one might expect, the energy of light emitted is proportional to the decrease in area, and therefore quantized. Because the energy of light is inversely proportional to its wavelength, only certain wavelengths of light are emitted.
In a previous article, I discussed a complete area spectrum that I proposed for blackholes. Using this area spectrum, one can easily determine the wavelengths of light that should be emitted by Hawking radiation. Therefore, if Hawking radiation is detected at LHC, it will either prove or falsify the area spectrum I obtained.