We consider the Gauss-Bonnet corrected Bardeen black hole solution in 4-D AdS space-time. The solution is obtained by the limiting procedure adopted by Glavan and Lin in 4-D Einstein-Gauss-Bonnet gravity. The general form of first law of black hole thermodynamics is utilized to calculate various thermodynamics variables. The solution exhibit P-v criticality and belong to the universality class of van-der Waals fluid. The effect of Gauss-Bonnet coupling is investigated on critical parameters and inversion temperature.
In this paper, we investigate the shadow radius and quasinormal modes of a four-dimensional magnetically charged Einstein-Gauss-Bonnet Bardeen black hole and point out a simple connection between them in the eikonal limit. By studying a massless scalar field perturbation in this spacetime background and using the sixth-order Wentzel-Kramers-Brillouin(WKB) approximation, we get the quasinormal modes(QNMs) and perform a detailed analysis. It shows that the quasinormal modes are depend on the Gauss-Bonnet coupling constant and the magnetic charge. We also give a formula of the QNMs and shadow rad…
We present a $D$-dimensional Bardeen like Anti-de Sitter (AdS) black hole solution in Einstein-Gauss-Bonnet (EGB) gravity, \textit{viz}., Bardeen-EGB-AdS black holes. The Bardeen-EGB-AdS black hole has an additional parameter due to charge ($e$), apart from mass ($M$) and Gauss-Bonnet parameter ($α$). Interestingly, for each value of $α$, there exist a critical $e = e_E$ which corresponds to an extremal regular black hole with degenerate horizons, while for $e< e_E$, it describes non-extremal black hole with two horizons. Despite the complicated solution, the thermodynamical quantities, like t…
We obtain exact Bardeen black holes to the regularized $4D$ Einstein--Gauss--Bonnet (EGB) gravity minimally coupled with the nonlinear electrodynamics (NED). In turn, we analyze the horizon structure to determine the effect of GB parameter $α$ on the minimum cutoff values of mass, $M_0$, and magnetic monopole charge, $g_0$, for the existence of a black hole horizon. We obtain an exact expression for thermodynamic quantities, namely, Hawking temperature $T_+$, entropy $S_+$, Helmholtz free energy $F_+$, and specific heat $C_+$ associated with the black hole horizon, and they show significant de…
Instead of the work \cite{1} which in according to the Lovelock theorem it could not applicable for all types of 4D curved spacetimes of Einstein Gauss Bonnet (EGB) gravity, authors of the work \cite{2} applied break of diffeomorphism property to present a consistent EGB gravity theory. In this work we use the latter model by adding a nonlinear electromagnetic field lagrangian density to study affects of GB coupling constant into the thermodynamic phase transition and Joule Thomson (JT) adiabatic expansion of a 4D $dS/AdS$ GB Bardeen black hole.
We study the $P-V$ criticality and phase transition in the extended phase space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black hole. The black holes can have a Ricci flat ($k=0$), spherical ($k=1$), or hyperbolic ($k=-1$) horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black holes, no $P-V$ criticality and phase transition appear, while for the black holes with a spherical horizon, even when the charge of the black …
We consider a charged Gauss-Bonnet black hole in $d$-dimensional spacetime and examine the effect of thermal fluctuations on the thermodynamics of the concerned black hole. At first we take the first order logarithmic correction term in entropy and compute the thermodynamic potentials like Helmholtz free energy $F$, enthalpy $H$ and Gibbs free energy $G$ in the spherical, Ricci flat and hyperbolic topology of the black hole horizon, respectively. We also investigate the $P$-$V$ criticality and calculate the critical volume $V_c$, critical pressure $P_c$ and critical temperature $T_c$ using dif…
In this article, we analytically investigate the microstructure of a five-dimensional neutral Gauss-Bonnet black hole, in the background of anti-de Sitter spacetime, using scalar curvature of the Ruppeiner geometry constructed via adiabatic compressibility. The microstructure details associated with the small-large black hole phase transition are probed in the parameter space of pressure and volume. The curvature scalar shows similar properties for both phases of the black hole, it diverges in the vicinity of critical point and approaches zero for extremal black holes. We show that the dominan…
We find an exact spherically symmetric regular Bardeen-like solutions by considering the coupling between Einstein-Gauss-Bonnet theory and nonlinear electrodynamics (NED) in five-dimensional spacetime. These solutions, with an additional parameter $g$ apart from the mass $M$, represent black holes with Cauchy and event horizons, extremal black holes with degenerate horizons or no black holes in the absence of the horizons, and encompasses as a special case Boulware-Deser black holes which can be recovered in the absence of magnetic charge ($g=0$). Owing to the NED corrected black hole, the the…
To provide an analytic verification of the nature of phase transition at the critical point of $P-V$ criticality, the original expressions of Ehrenfest equations have been introduced directly. By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we carry out analytical check of classical Ehrenfest equations. To show that our approach is universal, we investigate not only higher-dimensional charged AdS black holes, but also rotating AdS black holes. Not only are the examples of Einstein gravity shown, but also the example of modifie…
To understand the effect of third order Lovelock gravity, $P-V$ criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and details than the former literature. A detailed analysis of the limit case $β\rightarrow\infty$ is performed for the seven-dimensional black holes. It is shown that for the spherical topology, $P-V$ criticality exists for both the uncharged and charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P-V$ criticality. It may be att…
In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($Λ$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($α$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this univer…
The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure $P_{\mathrm{GB}}$. We studied the critical behavior associated with $P_{\mathrm{GB}}$ in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for Van der Waals system. For c…
Holographic CFT phase transitions and criticality for charged Gauss-Bonnet AdS black holes in the ensemble at fixed $(C, \mathcal{V}, \tilde{Q}, \tilde{\mathcal{A}})$
Observation indicates that many nearby galaxies host supermassive central black holes. Modelling Bardeen models in four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity, with additional parameters $\tildeα$ and charge $q$, as central black holes in various galaxies, we investigate gravitational lensing properties in strong deflection limits. Interestingly, the spherical photon orbit radius $x_m$, the critical impact parameter $u_m$, the lensing coefficient $\bar{b}$, the deflection angle $α_D(θ)$, angular position $θ_{\infty}$ are decreasing with $q$ and $α$ whereas the other lensing coeffic…
In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-García (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the Gauss-Bonnet theorem (GBT) and show that the deflection of light can be viewed as a partially topological effect in which the deflection angle can be calculated by considering a domain outside of the light ray applied to the black hole optical geometries. Then, we demonstrate also the deflection angle via the geodesics formalism for these black holes to verify our…
We derive an exact black hole solution for the Einstein-Gauss-Bonnet gravity with Yang-Mills field in $4D$ AdS spacetime and investigate its thermodynamic properties to calculate exact expressions for the black hole mass, temperature, entropy and heat capacity. The thermodynamic quantities get modification in the presence of Yang-Mills field, however, entropy remains unaffected by the Yang-Mills charge. The solution exhibits $P-v$ criticality and belongs to the universality class of Van der Waals fluid. We study the effect of Gauss-Bonnet coupling and Yang-Mills charge on the critical behaviou…
The EGB is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions, and EGB gravity is topologically invariant in $4D$. Several ways have been proposed for regularizing the $ D \to 4 $ limit of EGB for non-trivial gravitational dynamics in $ 4D $. Motivated by the importance of AdS/CFT, we obtain an exact static spherically symmetric nonsingular black hole in $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) in an AdS spacetime. We interpret the negative cosmological constant $Λ$ as the po…
New five-dimensional charged AdS black hole solutions are found in Einstein-Gauss-Bonnet gravity and the nonlinear electrodynamics. These solutions include regular black holes as well as extremal black holes. The first law of the black hole thermodynamics is confirmed in the extended phase space where the cosmological constant is treated as the pressure. The first and second order phase transitions are investigated by observing the behavior of the heat capacity at constant pressure and the Gibbs free energy. In addition, the equation of state for the black holes and their $P-V$ criticality are…
We investigate the thermodynamic behaviour of AdS quasitopological black hole solutions in the context of extended thermodynamic phase space, in which the cosmological constant induces a pressure with a conjugate volume. We find that the third order exact quasitopological solution exhibits features consistent with the third order Lovelock solutions for positive quasitopological coupling, including multiple reentrant phase transitions and isolated critical points. For negative coupling we find the first instances of both reentrant phase transitions and thermodynamic singularities in five dimens…
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
In this paper we study the thermodynamics of Einstein-Gauss-Bonnet (EGB)-AdS black holes minimally coupled to a cloud of strings in an extended phase space where the cosmological constant is treated as pressure of the black holes and its conjugate variable is the thermodynamical volume of the black holes. To investigate the analogy between EGB black holes surrounded by a cloud of strings and liquid-gas system we derive the analytical solutions of the critical points and probe the effects of a cloud of strings on $P-V$ criticality. There is obtained resemblance between "small black hole/large b…
We study third order Lovelock Gravity in $ D=7 $ at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in $ D=7 $ is less than t…
In this paper we construct an exact spherically symmetric black hole solution with a power Yang-Mills (YM) source in the context of $4D$ Einstein Gauss-Bonnet gravity ($4D$ EGB). We choose our source as $(F_{μν}^{(a)}F^{μν(a)})^q$, where $q$ is an arbitrary positive real number. Thereafter we study the horizon structure, thermodynamic issues like thermal stability and black hole phase transition of this black hole solution. Our focus here is to analyse the black hole space-time under the net non-linear effect coming both from the gravitational sector (due to Gauss-Bonnet term) as well as from …
Using the Gauss-Bonnet theorem, we compute and examine the deflection angle of light rays by rotating regular black holes with a cosmological constant. By the help of optical geometries, we first deal with the Hayward black holes with cosmological contributions. Then, we reconsider the study of the Bardeen solutions. We inspect the cosmological constant effect on the deflection angle of light rays. Concretely, we find extra cosmological correction terms generalizing certain obtained findings. Using graphical analysis, we provide a comparative discussion with respect to the Kerr solutions. The …
Geometrothermodynamics and critical behavior of regular black holes
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad Militar Nueva Granada（新格兰达军事大学基础科学学院数学系）；Departamento de Posgrado, CIIDET（CIIDET研究生院）
