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Schwarzschild Black Hole Quantum Statistics from Z(2) Orientation Degrees of Freedom and its Relations to Ising Droplet Nucleation | | H.A. Kastrup
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24 Jun 1999 | | Journal: | Annalen Phys. 9 (2000) 503-522 | | Subject: | General Relativity and Quantum Cosmology; Statistical Mechanics | gr-qc cond-mat.stat-mech hep-th | | Affiliation: | RWTH Aachen, Germany | | Abstract: | Generalizing previous quantum gravity results for Schwarzschild black holes from 4 to D > 3 space-time dimensions yields an energy spectrum E_n = alpha n^{(D-3)/(D-2)} E_P, n=1,2,..., alpha = O(1), where E_P is the Planck energy in that space-time. This spectrum means that the quantized area A_{D-2}(n) of the D-2 dimensional horizon has universally the form A_{D-2} = n a_{D-2}, where a_{D-2} is essentially the (D-2)th power of the D-dimensional Planck length. Assuming that the basic area quantum has a Z(2)-degeneracy according to its two possible orientation degrees of freedom implies a degeneracy d_n = 2^n for the n-th level. The energy spectrum with such a degeneracy leads to a quantum canonical partition function which is the same as the classical grand canonical partition function of a primitive Ising droplet nucleation model for 1st-order phase transitions in D-2 spatial dimensions. The analogy to this model suggests that E_n represents the surface energy of a "droplet" of n horizon quanta. Exploiting the well-known properties of the so-called critical droplets of that model immediately leads to the Hawking temperature and the Bekenstein-Hawking entropy of Schwarzschild black holes. The values of temperature and entropy appear closely related to the imaginary part of the partition function which describes metastable states | | Source: | arXiv, gr-qc/9906104 | | Services: | Forum | Review | PDF | Favorites | |
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