Inspired by the Lifshitz gravity as a theory with anisotropic scaling behavior, we suggest a new (n + 1)-dimensional metric in which the time and spatial coordinates scale anisotropically as (t, r, θ  i ) → (λ  z  t, λ  −1 r, λ  xi  θ  i ). Due to the anisotropic scaling dimension of the spatial coordinates, this spacetime does not support the full Schrödinger symmetry group. We look for the analytical solution of Gauss-Bonnet gravity in the context of the mentioned geometry. We show that Gauss-Bonnet gravity admits an analytical solution provided that the constants of the theory are properly adjusted. We obtain an exact vacuum solution, independent of the value of the dynamical exponent z, which is a black hole solution for the pseudo-hyperbolic horizon structure and a naked singularity for the pseudo-spherical boundary. We also obtain another exact solution of Gauss-Bonnet gravity under certain conditions. After investigating some geometrical properties of the obtained solutions, we consider the thermodynamic properties of these topological black holes and study the stability of the obtained solutions for each geometrical structure.

Iran

S. Mahmoudi

Kh. Jafarzade

Canada

S. Hendi

Gauss-Bonnet black holes in a special anisotropic scaling spacetime

Considering the variable cosmological constant in the extended phase space has a significant background in the black hole physics. It has been shown that the thermodynamic behavior of charged anti–de Sitter black hole surrounded by the quintessence in the extended phase space is similar to the van der Waals fluid. In this paper, we indicate that such a black hole admits the same criticality and van der Waals–like behavior in the nonextended phase space. In other words, we keep the cosmological constant as a fixed parameter, and instead, we consider the normalization factor as a thermodynamic variable. We show that there is a first-order small/large black hole phase transition which is analogous to the liquid/gas phase transition in fluids. We introduce a new picture of the equation of state and then we calculate the corresponding critical quantities. Moreover, we obtain the critical exponents and show that they are the same values as of the van der Waals system. Finally, we study the photon sphere and the shadow observed by a distant observer and investigate how the shadow radius may be affected by the variation of black hole parameters. We also investigate the relations between shadow radius and phase transitions and calculate the critical shadow radius where the black hole undergoes a second-order phase transition.

S. H. Hendi

Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space

Recently, there has been a surge of interest in the 4D Einstein-Gauss-Bonnet (4D EGB) gravity theory which bypasses the Lovelock theorem and avoids Ostrogradsky's instability. Such a novel theory has nontrivial dynamics and presents several predictions for cosmology and black hole physics. Motivated by recent astrophysical observations and the importance of anti-de Sitter spacetime (AdS), we investigate shadow geometrical shapes and deflection angle of light from the charged AdS black holes in 4D EGB gravity theory. We explore the shadow behaviors and photon sphere around such black holes, and inspect the effect of different parameters on them. Then, we present a study regarding the energy emission rate of such black holes and analyze the significant role of the Gauss-Bonnet (GB) coupling constant in the radiation process. Then, we perform a discussion of holographic heat engines of charged 4D EGB-AdS black holes by obtaining the efficiency of a rectangular engine cycle. Finally, by comparing heat engine efficiency with the Carnot efficiency, we indicate that the ratio <math><mfrac><mrow><mi>η</mi></mrow><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></mfrac></math> is always less than one which is consistent with the thermodynamic second law.