Vladan Pankovic, Darko Kapor
In this work, we suggest a simple thermodynamical (without any explicit use of the classical or quantum statistical distributions) and an approximate quantum theoretical, precisely "quasi-classical" formalism ("without knowing the details of quantum gravity", we paraphrase Fursaev). By this formalism we formally exactly reproduce final form of the Unruh temperature for a large, i.e. massive spherical physical system and Hawking temperature, Bekenstein-Hawking entropy, Bekenstein entropy/surface quantization for a Schwarzschild black hole. Finally, we reproduce satisfactorily approximately Hawking evaporation law for the Schwarzschild black hole. Our formalism holds the following suppositions. Firstly, we explicitly consider only quantum of the thermal radiation with average energy (from whole energetic, statistically distributed spectrum). Secondly, we suppose that circumference (of the great circle) of the large system or black hole horizon holds one reduced de Broglie wavelength of the average radiation quantum. (It is in some way similar to the Bohr orbital momentum quantization postulate for the ground state interpreted via de Broglie relation.) Finally, we suppose that (absolute value of the) potential energy of the gravitational interaction between large system and average radiation quantum is simply equivalent to product of the Boltzmann constant and temperature.
View original:
http://arxiv.org/abs/1011.1473
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