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Advances in High Energy Physics
Volume 2017, Article ID 1095217, 14 pages
Research Article

Thermodynamics of the Schwarzschild-AdS Black Hole with a Minimal Length

1School of Physics, Nankai University, Tianjin 300071, China
2Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, 14476 Potsdam, Germany

Correspondence should be addressed to Yan-Gang Miao; nc.ude.iaknan@gyoaim

Received 10 October 2016; Accepted 14 December 2016; Published 24 January 2017

Academic Editor: George Siopsis

Copyright © 2017 Yan-Gang Miao and Yu-Mei Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the -function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the -function and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the -function.