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Advances in High Energy Physics
Volume 2015 (2015), Article ID 124910, 11 pages
Research Article

Thermodynamic Relations for Kiselev and Dilaton Black Hole

1School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12, Islamabad 44000, Pakistan
2Department of Physics, Vivekananda Satavarshiki Mahavidyalaya, Vidyasagar University, Manikpara, Jhargram, West Midnapur, West Bengal 721513, India

Received 23 May 2015; Revised 12 August 2015; Accepted 19 August 2015

Academic Editor: George Siopsis

Copyright © 2015 Bushra Majeed et al. 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.


We investigate the thermodynamics and phase transition for Kiselev black hole and dilaton black hole. Specifically we consider Reissner-Nordström black hole surrounded by radiation and dust and Schwarzschild black hole surrounded by quintessence, as special cases of Kiselev solution. We have calculated the products relating the surface gravities, surface temperatures, Komar energies, areas, entropies, horizon radii, and the irreducible masses at the Cauchy and the event horizons. It is observed that the product of surface gravities, product of surface temperature, and product of Komar energies at the horizons are not universal quantities for the Kiselev solutions while products of areas and entropies at both the horizons are independent of mass of the above-mentioned black holes (except for Schwarzschild black hole surrounded by quintessence). For charged dilaton black hole, all the products vanish. The first law of thermodynamics is also verified for Kiselev solutions. Heat capacities are calculated and phase transitions are observed, under certain conditions.