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Advances in High Energy Physics
Volume 2017, Article ID 7158697, 13 pages
https://doi.org/10.1155/2017/7158697
Research Article

Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics

1Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454, Iran
2Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

Correspondence should be addressed to S. H. Hendi; ri.ca.uzarihs@idneh

Received 10 March 2017; Accepted 13 July 2017; Published 11 September 2017

Academic Editor: Giovanni Amelino-Camelia

Copyright © 2017 S. H. Hendi 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.

Abstract

Using the geometrical thermodynamic approach, we study phase transition of Brans–Dicke Born–Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies.