Abstract
Following previous study about AdS-Schwarzschild black holes minimally coupled to a cloud of strings in the context of massive gravity (Ghanaatian et al. in Effects of the external string cloud on the Van der Waals like behavior and efficiency of AdS-Schwarzschild black hole in massive gravity, arXiv:1906.00369 [hep-th]) and inspired by strong connection between Gauss–Bonnet Gravity and heterotic string theory, in this paper, we first take into account the Gauss–Bonnet term and we study thermodynamics and critical behavior of these black holes in the extended phase space. The effects of Gauss–Bonnet, massive, and string cloud parameters on the criticality of these black holes has been investigated. It can be seen that the Gauss–Bonnet and massive parameters have opposite effects on the criticality and phase transition of the solutions. We also observe that the increase in the value of the string cloud parameter above a critical value, eliminates the van der Waals like behavior of these solutions. Also, the Joule–Thomson effect is not observed. Then we examine thermal stability of these black holes in canonical ensemble by calculating the heat capacity. In addition, we explore critical behavior in extended phase space by employing heat capacity and consequently, we observe that the results are in agreement with the previous results from the usual method in Sect. 3.
Highlights
On the other hand, Einstein’s equation generally described an expanding universe, and Einstein first added a cosmological constant to his equation to describe a static universe
Cosmological constant is considered as a constant parameter, but on the contrary, in black hole thermodynamics is regarded as thermodynamic pressure which can vary
One of the promising theories in modern theoretical cosmology is the scalar-Einstein–Gauss–Bonnet gravity theory [13,14] which is motivated by string theory and shows how the string theory affects the primordial acceleration of the universe
Summary
Einstein’s equation generally described an expanding universe, and Einstein first added a cosmological constant to his equation to describe a static universe. If the cosmological constant is positive, the associated negative pressure will derive an accelerated expansion of the universe, as observed from the Planck Collaboration [4]. Cosmological constant is considered as a constant parameter, but on the contrary, in black hole thermodynamics is regarded as thermodynamic pressure which can vary. From this perspective, an extended phase space appears with a new dimension added, and the negative cosmological constant determines a positive varying thermodynamic pressure in this new framework. It was shown that the GB theory can be derived from the low-energy limit of heterotic string theory
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