By using the scattering of a scalar field, we discuss the thermodynamics and overcharging problem in a 4D Gauss-Bonnet AdS black hole in both the normal phase space and extended phase space. In the normal phase space, where the cosmological constant and Gauss-Bonnet parameter are fixed, the first law and the second law of thermodynamics are valid. In addiction, the black hole cannot be overcharged and the weak cosmic censorship conjecture is valid. In the extended phase space, where the cosmological constant and Gauss-Bonnet parameter are treated as the thermodynamic variables, the first law is still valid. However, the second law is indefinite. Moreover, after the scattering of the scalar field, the extremal black hole cannot be overcharged and the near-extremal black hole can be overcharged.
We study the thermodynamics in the grand canonical ensemble of D-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range $0<Φ<\frac{\sqrt{3}π}{4}$. For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom-AdS black holes, with …
By the Poincare sections, the dynamical behaviors of the ring string in the AdS-Gauss-Bonnet (AdS-GB) black hole are studied. A threshold value of the Gauss-Bonnet (GB) parameter $λ$ are found by the numerical method, below which the behavior of this dynamical system is no-chaotic and above which the behavior becomes gradually chaotic. The chaotic behavior becomes stronger with the increases of GB parameter. It is different from the case in the AdS-Schwarzschild black hole, which is weakly chaotic. Furthermore, we confirm our findings by the Fast Lyapunov indicators.
The topological classification of critical points of black holes in 4D Einstein-Gauss-Bonnet gravity coupled to Born-Infeld theory is investigated. Considered independently, Born-infeld corrections to the Einstein action alter the topological charge of critical points of the charged AdS black hole system, whereas the Gauss-Bonnet corrections do not. For the combined system though, the total topological charge of the Einstein-Gauss-Bonnet theory is unaltered in the presence of Born-Infeld coupling.
We construct solutions of a model which includes the Gauss-Bonnet and Born-Infeld terms for various horizon topologies $(k=0, \pm 1)$, and then the mass, temperature, entropy and heat capacity of black holes are computed. For the sake of simplicity, we perform the stability analysis of five dimensional topological black holes in AdS space.
In this paper, we show that the physical information given by conserved charges for asymptotically AdS spacetimes in Einstein-Gauss-Bonnet AdS gravity is encoded in the electric part of the Weyl tensor. This result generalizes the conformal mass definition by Ashtekar-Magnon-Das (AMD) to a gravity theory with a Gauss-Bonnet term. This proof makes use of the Noether charges obtained from an action renormalized by the addition of counterterms which depend on the extrinsic curvature (Kounterterms). If the asymptotic fall-off behaviour of the Weyl tensor is same as the one considered in the AMD me…
In this paper, the Joule{Thomson expansion of Born{Infeld AdS black holes in the consistent Aoki{Gorji{Mukohyama theory of 4D Einstein-Gauss-Bonnet gravity is studied in the extended phase space. We further analyze the effect of parameters αand βon the inversion curves and plot the inversion and isenthalpic curves in the T-P plane, which can determine the cooling-heating regions.
We study holographic superconductors in Einstein-Gauss-Bonnet gravity. We consider two particular backgrounds: a $d$-dimensional Gauss-Bonnet-AdS black hole and a Gauss-Bonnet-AdS soliton. We discuss in detail the effects that the mass of the scalar field, the Gauss-Bonnet coupling and the dimensionality of the AdS space have on the condensation formation and conductivity. We also study the ratio $ω_g/T_c $ for various masses of the scalar field and Gauss-Bonnet couplings.
By looking at the Lovelock theorem one can infer that the gravity model given by \cite{GL} could not applicable for all type of 4D Einstein Gauss Bonnet (GB) curved spacetimes. Because in 4D space time the Gauss-Bonnet invariant is a total derivative, and hence it does not contribute to the gravitational dynamics. Hence, authors in the work \cite{AL} presented an alternative consistent EGB gravity model instead of \cite{GL} by applying break of diffeomorphism property. In this work we use it to produce a dS/AdS black hole metric and then investigate its thermodynamic behavior in presence of cl…
In the spirit of the AdS/CFT correspondence, we investigate the hydrodynamics of the dual conformal field in the Gauss-Bonnet gravity. By considering the parameters of the boosted black brane in the Gauss-Bonnet gravity as functions of boundary coordinates, and then solving the corresponding correction terms, we calculate the first order stress-energy tensor of the dual conformal field. From this first order stress-energy tensor, we also obtain the shear viscosity and entropy density. And these results are consistent with those of some previous works from the effective coupling of gravitons.
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…
We find that AdS spacetime with a non-trivial linear dilaton field is an exact solution in the effective action of string theory, which is described by gravity with the Gauss-Bonnet curvature terms coupled to a dilaton field in the string frame. The AdS radius is determined by the spacetime dimensions and the coupling constants of curvature corrections. We also construct the asymptotically AdS black hole solutions with a linear dilaton field numerically. We discuss the thermodynamical properties of those solutions. Extending the model to the case with the even-order higher Lovelock curvature t…
With the help of the parametric solution of the Maxwell equal area law for the Gauss-Bonnet AdS black hole in five dimensions, we find the second analytical solution to the first order phase transition. We analyze the asymptotic behaviors of some characteristic thermodynamic properties for the small and large black holes at the critical and zero temperatures and also calculate the critical exponents and the corresponding critical amplitudes in detail. Moreover, we give the general form of the thermodynamic scalar curvature based on the Ruppeiner geometry and point out that the attractive inter…
A finite action principle for Einstein-Gauss-Bonnet AdS gravity is presented. The boundary term, which is different for even and odd dimensions, is a functional of the boundary metric, intrinsic curvature and extrinsic curvature. For even dimensions, the boundary term corresponds to the maximal Chern form of the spacetime, and the asymptotic AdS condition for the curvature suffices for the well-posedness of this action. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. The background-independent Noether charges associated to as…
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.
AdS spacetime has been shown numerically to be unstable against a large class of arbitrarily small perturbations. In arXiv:1410.1869, the authors presented a preliminary study of the effects on stability of changing the local dynamics by adding a Gauss-Bonnet term to the Einstein action. Here we provide further details as well as new results with improved numerical methods. In particular, we elucidate new structure in Choptuik scaling plots. We also provide evidence of chaotic behavior at the transition between immediate horizon formation and horizon formation after the matter pulse reflects f…
In this work, we present the quasinormal modes of a fermionic field in the background of Gauss-Bonnet-AdS black holes. We find exact solutions for $D=5$ at the fixed value $α=R^2/2$ of the Gauss--Bonnet coupling constant, with $R$ denoting the AdS radius, and we find numerical solutions for some range of values of the coupling constant $α$ and $D=5, 6$. Mainly, we find two branches of quasinormal frequencies, a branch perturbative in the Gauss-Bonnet coupling constant $α$, and another branch nonperturbative in $α$. The phenomena of nonperturbative modes, which seem to be quite general in theor…
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…
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…
Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the spacetime is too small, thereby restoring the stabilit…
This work is devoted to the exploration of shadow cast and center of mass energy in the background of a 4-dimensional charged Gauss-Bonnet AdS black hole. On investigating particle dynamics, we have examined BH's metric function. Whereas, with the help of null geodesics, we pursue to calculate the celestial coordinates and the shadow radius of the black hole. We have made use of the hawking temperature to study the energy emission rate. Moreover, we have explored the center of mass energy and discussed its characteristics under the influence of spacetime parameters. For a better understanding,…
In this paper, we study the thermodynamic geometry of charged Gauss-Bonnet black holes (and Reissner-Nordström black holes, for the sake of comparison) in AdS: in both $(T,V)$- and $(S,P)$-planes. The thermodynamic phase space is known to have an underlying contact and metric structure; Ruppeiner geometry then naturally arises in this framework. Sign of Ruppeiner curvature can be used to probe the nature of interactions between the black hole microstructures. It is found that there are both attraction and repulsion dominated regions which are in general determined by the electric charge, Gauss…
We investigate the holographic fermions in the charged Gauss-Bonnet $AdS_{d}$ black hole background with the dipole coupling between fermion and gauge field in the bulk. We show that in addition to the strength of the dipole coupling, the spacetime dimension and the higher curvature correction in the gravity background also influence the onset of the Fermi gap and the gap distance. We find that the higher curvature effect modifies the fermion spectral density and influences the value of the Fermi momentum for the appearance of the Fermi surface. There are richer physics in the boundary fermion…
In this paper, we analytically study the phase structure and construct the Ruppeiner geometry in the extended phase space for the five-dimensional neutral Gauss-Bonnet AdS black hole. Through calculating the scalar curvature of the Ruppeiner geometry and combining the phase transition, we show that the attractive interaction is dominant in the microstructure of the black hole system. More significantly, there is an intriguing property that the normalized scalar curvature has the same expression for the saturated small and large black hole curves. This implies that although the microstructure i…
Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity $η$, entropy density $s$, thermal conductivity $κ$ and …
Recently a non-trivial 4-dimensional theory of gravity that claims to circumvent Lovelock's theorem and avoid Ostrogradsky instability was formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)]. This theory, named "$4D$ Einstein Gauss-Bonnet gravity", presents several novel predictions for cosmology and black hole physics. In this paper, we generalize the vacuum black hole solution of Glavan \& Lin to include electric charge in an anti-de Sitter space and explore some properties of this solution such as the asymptotics, properties of the horizons, the general relativity limi…
We present \emph{area (or entropy) functional relation} for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is \emph{mass-independent} whereas the entropy product relation is \emph{not} mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. \emph{Smarr mass formula} and \emph{first law} of thermodynamics have been derived. This \emph{mass-independent} relation sugge…
It is well-known that there exists a Hawking-Page phase transition between a spherical AdS black hole and a thermal AdS space. The phase transition does not happen between a Ricci flat AdS black hole whose horizon is a Ricci flat space and a thermal AdS space in the Poincare coordinates. However, the Hawking-Page phase transition occurs between a Ricci flat AdS black hole and an AdS soliton if at least one of horizon coordinates for the Ricci flat black hole is compact. We show a similar phase transition betwen the Ricci flat black holes and deformed AdS solitons in the Gauss-Bonnet gravity an…
Using a modified expression for the electric potential in the context of T-duality (Gaete and Nicolini, Phys. Lett. B, 2022) we obtain an exact charged solution within 4D Einstein-Gauss-Bonnet (4D EGB) theory of gravity in the presence of a cosmological constant. We show that the solution exists in the regularized 4D EGB theory as well and we point out a correspondence between the black hole solution in 4D EGB theory and the solution in the non-relativistic Horava--Lifshitz theory. The black hole solution is regular and free from singularity and as a special case we recover a class of well-kno…
We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics (NED). These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy o…
Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of spacetime in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in [5] for the higher curvature corrected black hole with the pl…
Based on superconformal tensor calculus in five dimensions, we construct the supersymmetric completion of Gauss-Bonnet combination. We study the vacuum solutions with AdS_2 x S^3 and AdS_3 x S^2 structures. We also analyze the spectrum around a maximally supersymmetric Minkowski_5.
We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the dilaton and a negative ``cosmological constant''. We derive the field equations for the static spherically symmetric ($k=1$) and hyperbolically symmetric ($k=-1$) spacetime in general $D$ dimensions. The system has some scaling symmetries which are used in our analysis of the solutions. We find exact solutions, i.e., regular AdS solution for $k=1$ and a massless black hole solution for $k=-1$. Nontrivial asymptotically AdS solutions are obtained numerically in D=4 -- 6 and 10 dimensional spacetimes. For spherically sym…
Thermalons can mediate phase transitions between different vacua in higher curvature gravity, potentially changing the asymptotic structure of the spacetime. Treating the cosmological constant as a dynamical parameter, we study these phase transitions in the context of extended thermodynamic phase space. We find that in addition to the AdS to dS phase transitions previously studied, thermal AdS space can undergo a phase transition to an asymptotically flat black hole geometry. In the context of AdS to AdS transitions, we comment on the similarities and differences between thermalon transitions…
It has recently been found that quasinormal modes of asymptotically anti-de Sitter (AdS) black holes in theories with higher curvature corrections may help to describe the regime of intermediate 't Hooft coupling in the dual field theory. Here, we consider quasinormal modes of a scalar field in the background of spherical Gauss--Bonnet--anti-de Sitter (AdS) black holes. In general, the eigenvalues of wave equations are found here numerically, but at a fixed Gauss-Bonnet constant $α= R^2/2$ (where $R$ is the AdS radius), an exact solution of the scalar field equation has been obtained. Remarkab…
Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling $α$. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in $α$ correction to the damping rates: $ω\approx Re(ω_{SAdS}) - Im(ω_{SAdS…
The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field $b$ makes it easier for the scalar hair to be condensated; ii) the ratio of the gap frequency in conductivity $ω_g$ to the critical temperature $T_c$ depends on both $b$ and the Gauss-Bonnet constant $α$; and iii) the critical exponents are…
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, 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 inspe…
The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the …
Motivated by possible applications within the framework of anti-de Sitter gravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by a nonlinear electrodynamics (NED) are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedur…
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 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…
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant $Λ$. First, for $Λ\le 0$ and $α\ge 0$ without a fine-tuning to give a unique anti-de Sitter vacuum, where $α$ is the Gauss-Bonnet coupling constant, vanishing generalized Misner-Sharp mass is equivalent to the maximally symmetric spacetime. Under the fine-tuning, it is equivalent to the vacuum class I spacetime. Second, under the fine-tuning with $α>…
We study asymptotically AdS topological black hole solutions with k=0 (plane symmetric) in the Einstein gravity with Gauss-Bonnet term, the dilaton and a "cosmological constant" in various dimensions. We derive the field equations for suitable ansatz for general D dimensions. We determine the parameter regions including dilaton couplings where such solutions exist and construct black hole solutions of various masses numerically in D=4,5,6 and 10 dimensional spacetime with (D-2)-dimensional hypersurface of zero curvature.
The Van der Waals-like phase transition is observed in temperature-thermal entropy plane in spherically symmetric charged Gauss-Bonnet-AdS black hole background. In terms of AdS/CFT, the non-local observables such as holographic entanglement entropy, Wilson loop, and two point correlation function of very heavy operators in the field theory dual to spherically symmetric charged Gauss-Bonnet-AdS black hole have been investigated. All of them exhibit the Van der Waals-like phase transition for a fixed charge parameter or Gauss-Bonnet parameter in such gravity background. Further, with choosing v…
We employ the variational method for the Sturm-Liouville eigenvalue problem to analytically study the phase transition between the holographic insulator and superconductor in the Gauss-Bonnet gravity. By investigating the s-wave and p-wave holographic insulator/superconductor models, we find that this analytic method is more effective to obtain the analytic results on the condensation and the critical phenomena in the AdS soliton background in Gauss-Bonnet gravity. Our analytic result can be used to back up the numerical computations in the AdS soliton with Gauss-Bonnet correction.
Motivated by recent work, nonmonotonic behaviours of photon sphere radius can be used to reflect black hole phase transition for Reissner-Nordstr$\ddot{o}$m-AdS (RN-AdS) black holes, we study the case of five-dimensional charged Gauss-Bonnet-AdS (GB-AdS) black holes in the reduced parameter space. We find that the nonmonotonic behaviours of photon sphere radius still exist. Using the coexistence line calculated from $P-V$ plane, we capture the photon sphere radius of saturated small and large black holes (the boundary of the coexistence phase), then illustrate the reduced coexistence region. T…
We obtain an exact solution of $AdS$ black hole solution in Einstein-Gauss-Bonnet (EGB) gravity coupled with nonlinear electrodynamics. It interpolates with the $AdS$ regular black hole and $AdS$ EGB black hole in the absence of the Gauss-Bonnet coupling constant and both magnetic monopole charge and deviation parameter, respectively. Based on horizon thermodynamics, we study the thermodynamic properties of the obtained solution (e.g. mass, temperature, entropy, heat capacity and free energy). The Hawking temperature of the nonsingular black hole gets the maximum value at the point where speci…
In this paper, the new formalism of thermodynamic geometry proposed in [1] is employed in investigating phase transition points and the critical behavior of a Gauss Bonnet-AdS black hole in four dimensional spacetime. In this regard, extrinsic and intrinsic curvatures of a certain kind of hypersurface immersed in the thermodynamic manifold contain information about stability/instability of heat capacities. We, therefore, calculate the intrinsic curvature of the $Q$-zero hypersurface for a four-dimensional neutral Gauss Bonnet black hole case in the extended phase space. Interestingly, intrinsi…
Einstein-Gauss-Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein-Gauss-Bonnet gravity in various spacetime dimensions with both positive and negative couping constant $α$. By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $α>0$, i…
