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In this paper, we investigated new solutions for the anisotropic compact stellar model in Einstein–Gauss–Bonnet (EGB) theory. In this context, we established a set of field equations with the help of anisotropic matter configuration. The relation between pressure in the radial direction and the energy density is taken by using a linear equation of state (EoS). A well-known Boulware–Deser exterior spacetime is matched with interior spherically symmetric spacetime at the boundary of the star to determine the unknown parameters. Different physical parameters are investigated, namely, these are density, radial pressure and transversal pressure, anisotropy, mass function, compactness and surface redshift. We discussed Herrera’s cracking condition, Tolman–Oppenheimer–Volkoff (TOV), and the adiabatic index. The values of some physical quantities like density (at center and surface), compactness and surface redshift are calculated numerically for three compact stars PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451. A graphical analysis of these physical quantities for a representative compact star candidate PSR J0348+0432 is also presented with various values of EGB parameter α. The energy conditions for anisotropic compact star PSR J0348+0432 are satisfied, surface redshift remains within the limit and also all the stability conditions that we discussed in this work are satisfied, this validates our presented model. The effects of the GB coupling parameter α on the physical parameters are depicted graphically and numerically. [ABSTRACT FROM AUTHOR]

We study the thermal decoupling of weakly interacting massive particles (WIMPs) in a dilatonic Einstein Gauss–Bonnet (dEGB) cosmological scenario where standard gravity is modified by a Gauss–Bonnet term non-minimally coupled to a scalar field with vanishing potential. We put constraints on the parameters of the model that drive the WIMP annihilation cross section beyond the present bounds from DM indirect detection searches. The bounds from WIMP indirect detection are nicely complementary to late-time constraints from compact binary mergers. This suggests that it could be interesting to use other Early Cosmology processes to probe the dEGB scenario. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the analysis of the f (R , T) -brane via the inclusion of a term proportional to the Gauss–Bonnet invariant. We consider an action of the form F (R , G , T) = f (R , T) + α G , where T is the trace of the stress–energy tensor, R is the Ricci scalar, and α is a real parameter that controls the contribution of the Gauss–Bonnet invariant G. We introduce the first-order formalism to obtain solutions for the source field of the brane in the special case where f (R , T) = R + β T and illustrate its procedure with an application to the sine-Gordon model. We also investigate the general case of the f (R , T) -brane via the use of the scalar–tensor formalism, where we also use the first-order formalism to obtain solutions. Finally, we investigate the linear stability of the brane under tensor perturbations of the the modified Einstein's field equations. Our results indicate that the Gauss–Bonnet term may induce qualitatively different behaviors of the quantities on the brane, provided that its contribution is large enough. [ABSTRACT FROM AUTHOR]

In addition to the classical definition of the black hole’s entropy, quantum mechanics requires several modifications of it. In this article, we consider the higher-order quantum correction in entropy and analyze the thermodynamic properties of a black hole solution which is sitting in one of the modified gravity theories, viz. Gauss-Bonnet gravity, in this point of view. Here mainly two thermodynamic potentials, Gibbs free energy and Helmholtz free energy are studied. As both potentials are very much important to investigate small/large black hole phase transition. Presenting the variations of higher-order corrected Gibbs free energy and Helmholtz free energy in different conditions, we analyze the phase transition and critical behavior of said black holes. We also re-examine our results, with the P - V criticality analyses and study P - r + diagrams. Moreover, we compute the critical temperature, pressure and volume and the relation among them. Here we find an interesting result for Q = 0 and for the Ricci flat horizon of this black hole that the relation is exactly equal to the result obtained for the van der Waals system. Further, we study thermal stability by computing the specific heat with higher-order correction and explain it by depicting the C HC vs r + diagrams in different conditions. [ABSTRACT FROM AUTHOR]

To better understand the effects of strong coupling and QCD at high temperature in QGP, by using holographic model, we investigate the dissociation effect of bottomonium under the higher-order curvature corrections to the supergravity action corresponding to the corrections of large N expansion of boundary CFT in the side of field theory. The results show that effective potential is not a good physical quantity to estimate the dissociation strength of bottomonium in the case of finite wave number and considering the higher-order curvature corrections. Therefore, we calculate the quasinormal spectra (QNMs) and the differential configuration entropy (DCE). It is found that the dissociation effect is stronger for the stronger coupling.

This work provides the exact solution of the Bardeen black hole in association with 4 D Gauss–Bonnet massive gravity in Anti-de-Sitter (A d S) space–time. It is a modification of the Gauss–Bonnet when gravity couples with nonlinear matter fields which is the function of the electromagnetic field. The obtained solution gives rise to 4 D EGB Bardeen black holes when the massive gravity parameter is set to zero and it yields a 4 D Gauss–Bonnet black hole in the absence of magnetic monopole charge. Further, we analyze and adopt the thermodynamic quantities like mass ( M + ), temperature (T +) and heat capacity (C +) in the presence of massive gravity and nonlinear electrodynamics. In addition, we extend our results by considering the cosmological constant (Λ) as a thermodynamical variable (P = − Λ / 8 π) and obtain the critical values of pressure, temperature, horizon radius and analyze the behavior of the global parameter P c v c / T c . The effect of a massive parameter (m) of the critical exponent is opposite to the magnetic monopole charge (e) and Gauss–Bonnet parameter (α). According to our analysis the phase transition between a small and large black hole and van der Waals phase transition are analogous to each other. [ABSTRACT FROM AUTHOR]

In this paper, we treat 4-dimensional Einstein–Gauss–Bonnet (EGB) gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer–Snyder–Datt model of the gravitational collapse of a star in a 4-dimensional EGB black hole (BH). The inside geometry of the star is described by the spatially flat Friedmann–Robertson–Walker metric and the matter is distributed uniformly without any pre-assumption about its equation of state. The exterior EGB BH is smoothly matched to the interior geometry without the requirement of any thin shell. This gives the energy density, pressure, and the equation of state of collapsing matter. At the end, we study the time evolution of event and apparent horizons. [ABSTRACT FROM AUTHOR]

We study a number of well-motivated theories of modified gravity with the common overarching theme that they predict the existence of compact objects, such as black holes and wormholes endowed with scalar hair. We compute the shadow radius of the resulting compact objects and demonstrate that black hole images, such as that of M87 * or the more recent SgrA * by the Event Horizon Telescope (EHT) collaboration, could provide a powerful way to constrain deviations of the metric functions from what is expected from general relativity (GR) solutions. We focus our attention on Einstein-scalar-Gauss–Bonnet (EsGB) theory with three well-motivated couplings, including the dilatonic and Z 2 symmetric cases. We then analyze the shadow radius of black holes in the context of the spontaneous scalarization scenario within EsGB theory with an additional coupling to the Ricci scalar (EsRGB). Finally, we turn our attention to spontaneous scalarization in the Einstein–Maxwell-Scalar (EMS) theory and demonstrate the impact of the parameters on the black hole shadow. Our results show that black hole imaging is an important tool for constraining black holes with scalar hair, and, for some part of the parameter space, black hole solutions with scalar hair may be marginally favored compared to solutions of GR. [ABSTRACT FROM AUTHOR]

The latest findings of static and spherically symmetric black hole solution give a potential platform to investigate the novel four-dimensional Einstein Gauss–Bonnet gravity. In order to obtain a rotating black hole solution, we first adopt the Newman Janis algorithm and study the structure of its horizons. To analyze the said black hole shadow, we move forward to compute expressions of the celestial coordinates using the geodesic equations. Furthermore, we provide a detailed analysis of the shadow size and its distortion parameter, adopting the Hioki and Maeda method, together with the applications of a supermassive black hole shadow in the center of nearby galaxy Messier 87 and obtained constraints on the relationships of spin and charge. From the obtained results, we demonstrate that both spin and coupling parameters of the black hole have a substantial influence on shadow structure. The increment in the values of these parameters diminishes the shadow radius. We also study the energy emission rate using the Hawking temperature. Furthermore, it is shown that whenever the collision of two electrically neutral test particles takes place in the vicinity of the black hole horizon, the Gauss–Bonnet black hole may serve as a particle accelerator with an infinitely large center of mass energy. [ABSTRACT FROM AUTHOR]

We present a flat emergent universe model in modified Gauss–Bonnet gravity in four dimensions. The emergent universe model is free from a big-bang singularity and also describes the observed universe fairly well. It is assumed that the present universe emerged from a static Einstein universe phase that exists in the infinite past. To obtain the flat emergent universe model, we reconstruct mimetic modified f (G) -gravity (G representing Gauss–Bonnet terms). The functional form of f (G) -gravity is determined with or without matter, and can accommodate the early inflation and late accelerating phases satisfactorily. In contrast, in Einstein's general theory of relativity, a flat emergent universe was obtained within the modified matter sector. [ABSTRACT FROM AUTHOR]

Using the Newman–Janis algorithm, we study certain optical behaviors of rotating quintessential black holes in Einstein Gauss–Bonnet gravity models with a cloud of strings. Concretely, we investigate the shadow behaviors in terms of one dimensional real curves. By elaborating the associated null geodesic equations of motion, we illustrate the shadow geometries in terms of an appropriate moduli space involving external dark field contributions. Among others, we find that the string cloud parameter serves as a geometric quantity controlling the shadow size. We approach graphically the corresponding astronomical observables. Then, we compute and analyze the energy emission rate by varying the involved parameters. Finally, we discuss a possible connection with observations from Event Horizon Telescope by providing certain constraints on the involved black hole parameters in the light of the M 87 ∗ image. [ABSTRACT FROM AUTHOR]

The entanglement wedge cross section (EWCS) is numerically investigated statically and dynamically in a five-dimension AdS-Vaidya spacetime with Gauss-Bonnet (GB) corrections, focusing on two identical rectangular strips on the boundary. In the static case, EWCS increases as the GB coupling constant α increases and disentangles at small separation between two strips for smaller α. For the dynamic case, such a monotonic relationship between EWCS and α holds but the two strips no longer disentangle monotonically as in the static case. In the early thermal quenching stage, the disentanglement occurs at smaller α with larger separations. Two strips then disentangle at larger separation with larger α as time evolves. Our results indicate that the higher-order derivative corrections, like the entanglement measure in the dual boundary theory, also have nontrivial effects on the EWCS evolution. [ABSTRACT FROM AUTHOR]

We make use of the Hamilton–Jacobi and Parikh-Wilczek methods to investigate the Hawking radiation from the event horizon of a new charged anti-de Sitter black hole in four-dimensional Gauss-Bonnet gravity space–time. Both the tunneling rate of charged particles and the Bekenstein-Hawking entropy are evaluated. The emission spectrum is an impure thermal one and consistent with an underlying unitary theory. There is no difference between the emission rate of massive particle and that of massless one. The entropy is modified by a logarithmic term so that the area law of the black hole entropy is violated. It satisfies the first law of black hole thermodynamics and has the same expression as that calculated by Loop Quantum Gravity and String Theory. When the Gauss-Bonnet coupling coefficient is equal to zero, the logarithmic correction vanishes and the Bekenstein-Hawking relation in general relativity is recovered. So our results show the effects of the Gauss-Bonnet modified gravity on the Bekenstein-Hawking entropy and Hawking radiation. [ABSTRACT FROM AUTHOR]

In this paper, we analytically present an exact confining charged black hole solution to the scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity (4DEGBG) coupled to non-linear gauge theory containing −F2 term. Part of the importance of using a non-trivial 4D theory of Gauss-Bonnet gravity is that it is proven the absence of the Ostrogradsky instability was formulated in Glavan and Lin (2020) [26] and then regularized 4DEGBG theory was obtained in Hennigar et al. (2020) [45] and Fernandes et al. (2020) [49] as well as this theory gains many attentions because of its important finding for black hole physics. We therefore also study some properties of this solution such as temperature, specific heat, shadow and quasinormal modes. Our results here show that a confining charge f gives a significant contribution to the shadow of the black hole as well as quasinormal modes frequencies.

Various proposals for gravitational entropy densities have been constructed from the Weyl tensor. In almost all cases, though, these studies have been restricted to general relativity, and little has been done in modified theories of gravity. However, in this paper, we investigate the simplest proposal for an entropy density constructed from the Weyl tensor in five-dimensional Gauss–Bonnet gravity and find that it fails to reproduce the expected entropy of a black hole. [ABSTRACT FROM AUTHOR]

In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with N order of derivatives and M rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for N = M = 1 and linearized Gauss–Bonnet gravity for N = M = 2. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell's theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell's theory, the first invariant derived from the procedure in N = M = 2 can be introduced. The complete gauge invariance of a model with respect to Noether's first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin- n curvature tensors for all N = M = n are the field strength tensors for each n. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature. [ABSTRACT FROM AUTHOR]

The stability of two different bounce scenarios from F (R , 𝒢) modified gravity at later times is studied, namely a hyperbolic cosine bounce model and a matter-dominated one. After describing the main characteristics of F (R , 𝒢) modified gravity, the two different bounce scenarios stemming from this theory are reconstructed and their stability at late stages is discussed. The stability of the hyperbolic cosine model is proven, while the concrete matter-bounce model here chosen does not seem to accomplish the necessary conditions to be stable at later times. [ABSTRACT FROM AUTHOR]

In this paper, the solutions of the Gauss-Bonnet theory of gravity was proposed in the presence of a perfect fluid with thermodynamic pressure P and energy gravity ρ in n-dimension. Accordingly, perfect fluid tensor was regarded as energy-momentum tensor and the static and radiating solutions for the linear equation of state p = wρ was calculated. This solution contains all the solutions already being proposed for Gauss-Bonnet gravity, such as asymptotically flat or asymptotically uncharged (anti)-de Sitter, radiating asymptotically flat and (anti)-de Sitter solutions as well as some new static and radiating solutions for different w values. We go through the properties of the new static and radiating solutions. We find solutions for w = 0 and w = (n-2)-2 in static and radiating states. We also show that the solutions satisfy the dominant and weak energy conditions and they present black holes with one or two horizons or naked singularities provided that the parameters of the solutions are chosen suitable.

In this paper, the holographic superconductor model with two s-wave orders from 4+1 dimensional Einstein–Gauss–Bonnet gravity is explored in the probe limit. At different values of the Gauss–Bonnet coefficient α, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s + s coexistent phase, including the reentrant phase transition near the Chern–Simons limit α=0.25, can be found. We also give an explanation to the nontrivial behavior of the Tc–α curves near the Chern–Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern–Simons limit.

This paper deals with spherically symmetric gravitational collapse of inhomogeneous perfect fluid in Einstein Gauss–Bonnet gravity. The physical quantities have been plotted in the EGB gravity. The Ricci Scalar and Kretschmann scalar have been determined to study the curvature singularity. The shell focusing curvature singularities are generated at last stage of gravitational collapse of object. The formation of singularity and apparent horizon depends on the initial data. Also, the energy conditions have been discussed for the reasonable energy momentum tensor. The presence of GB coupling constant α modifies the structure of singularity and formation of apparent horizon. [ABSTRACT FROM AUTHOR]

We construct a new class of stationary exact solutions to five-dimensional Einstein–Gauss–Bonnet gravity. The solutions are based on four-dimensional self-dual Atiyah–Hitchin geometry. We find analytical solutions to the five-dimensional metric function that are regular everywhere. We find some constraints on the possible physical solutions by investigating the solutions numerically. We also study the behavior of the solutions in the extremal limits of the Atiyah–Hitchin geometry. In the extremal limits, the Atiyah–Hitchin metric reduces to a bolt structure and Euclidean Taub–NUT space, respectively. In these limits, the five-dimensional metric function approaches to a constant value and infinity, respectively. We find that the asymptotic metrics are regular everywhere. [ABSTRACT FROM AUTHOR]

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge-invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives (N) and a rank of tensor potential (M), then solving such that the model is completely gauge-invariant (the Lagrangian density, equation of motion and energy–momentum tensor are all gauge-invariant). In the case of N = 1 order of derivatives and M = 1 rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of N = 2 order of derivatives and M = 2 rank of symmetric tensor potential, linearized Gauss–Bonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized Gauss–Bonnet gravity from a common set of rules provides an interesting connection between two well-explored physical models. [ABSTRACT FROM AUTHOR]

In this work, we have studied the effects of dissipative viscous/heat gravitational collapse on the dynamics of collapsing source in 5D Einstein–Gauss–Bonnet theory using full casual approach. For this purpose, the dynamical equations have been formulated by using Misner–Sharp approach in 5D Einstein–Gauss–Bonnet theory of gravity. Using the Müller–Israel–Stewart theory, the dynamical equations have coupled with casual transport equations for the heat flux, the bulk and shear bulk viscosity to determine the effects of heat flux including thermodynamics viscous/heat coupling coefficients. The applications of this work to certain astrophysical situations are discussed. [ABSTRACT FROM AUTHOR]

Einstein gravity supplemented by a scalar field nonminimally coupled to a Gauss–Bonnet term provides an example of model of scalar-tensor gravity where hairy black holes do exist. We consider the classical equations within a metric endowed with a NUT-charge and obtain a two-parameter family of nutty-hairy black holes. The pattern of these solutions in the exterior and the interior of their horizon is studied in some details. The influence of both — the hairs and the NUT-charge — on the lightlike and timelike geodesics is emphasized. [ABSTRACT FROM AUTHOR]

In this paper, we shall analyze the gravity phase space, in the case that the corresponding dynamical system is autonomous. In order to make the dynamical system autonomous, we shall appropriately choose the independent variables, and we shall analyze the evolution of the variables numerically, emphasizing on the inflationary attractors. As we demonstrate, the dynamical system has only one de Sitter fixed point, which is unstable, with the instability being traced in one of the independent variables. This result holds true both in the presence and in the absence of matter and radiation perfect fluids. We argue that this instability could loosely be viewed as an indication of graceful exit in the theory of gravity. [ABSTRACT FROM AUTHOR]

This work investigates the thermodynamics, phase transition, and topological classes of Neutral Gauss–Bonnet (GB) AdS black holes (BHs) in 5D. We obtain equations for several thermodynamic quantities for the Neutral GB of AdS BHs by using the well-known properties of BH thermodynamics. We find thermal stability and other significant thermodynamical parameters that assist us study stability and criticality. Thermodynamic features of Neutral GB AdS BHs are graphically explored by utilizing (C p) , (T − S) , (P − r h) , and G , volume expansivity (β), isothermal compressibility (κ). Second-order phase transitions, like C p − S illustrates the divergence behavior. In addition, the swallow tail behavior finds the stability and instability of small black holes (SBH), intermediate black holes (IBH), and large black holes (LBH). Also, our investigation focuses on analyzing the topology of thermodynamic critical points and calculating their respective topological charges within the canonical and grand canonical ensembles. This analysis allows us to discuss the ensemble dependence of the Neutral GB-AdS BH exists. • Thermodynamics, phase transition and topological classes of BHs in 5 D are discussed. • We find thermal stability and other significant thermodynamical parameters. • The swallow-tail behavior finds the stability and instability of SBH, IBH, and LBH. • Analyze the topology of thermodynamic critical points and topological charges. • This analysis allows us to discuss the ensemble dependence neutral GB-AdS BH exists. [ABSTRACT FROM AUTHOR]

We discuss black hole type solutions and wormhole type ones in the effective gravity models. Such models appear during the attempts to construct the quantum theory of gravity. The mentioned solutions, being, mostly, the perturbative generalisations of well-known ones in general relativity, carry out additional set of parameters and, therefore could help, for example, in the studying of the last stages of Hawking evaporation, in extracting the possibilities for the experimental or observational search and in helping to constrain by astrophysical data.

We extend the Parikh-Wilczek method from Einstein gravity spacetime to Gauss-Bonnet modified gravity and study the tunneling radiation of particles across the event horizon of a d-dimensional Gauss-Bonnet Anti de-Sitter black hole. The emission rate of a particle is calculated. It is shown that the emission rate of massive particles takes the same functional form as that of massless particles although that their motion equations tunneling across the horizon are different. It is also shown that the emission spectrum deviates from the pure thermal spectrum but is consistent with an underlying unitary theory. In addition, significant but interesting phenomenon is demonstrated when Gauss-Bonnet term is present. The expression of the emission rate for a black hole in Gauss-Bonnet gravity differs from that for a black hole in Einstein gravity. After adopting the conventional tunneling rate, we obtain the expression of the entropy of the Gauss-Bonnet black hole, which is in accordance with the early results but does not obey the area law. So the research of tunneling radiation in this paper may serve as a new perspective of understanding the thermodynamics of black holes in Gauss-Bonnet gravity. [ABSTRACT FROM AUTHOR]

Taking into account the perturbative corrections of Einstein (EN)-Maxwell gravity, we study thermodynamical behavior of the black holes in the context of geometrical thermodynamics (GT). We consider a quadratic Maxwell invariant as a correction of Maxwell theory in electromagnetic viewpoint and Gauss-Bonnet (GB) gravity as a correction of EN theory in gravitational point of view. We study thermodynamical phase transition and show that employing Weinhold, Ruppeiner and Quevedo approaches fails to produce desirable results. Next, Hendi-Panahiyan-Eslam Panah-Momennia (HPEM) metric will be employed in order to study GT of the solutions. We show that this metric is capable of matching all the divergence points of its thermodynamical curvature scalar with phase transition and bound points. Moreover, the effects of the variation of different parameters on phase transition points will be investigated. [ABSTRACT FROM AUTHOR]

We demonstrate that the intermediate inflation scenario is a singular inflation cosmology, with the singularity at the origin t = 0 being a pressure and energy density singularity and particularly a Type III singularity. Also, we show that the expanding phase of a singular bounce can be identical to the intermediate inflation scenario, if the singular bounce has a Type III singularity at the origin. For the intermediate inflation scenario we examine the cosmological implications on the power spectrum in the context of various forms of modified gravity. Particularly, we calculate the power spectrum in the context of F( R), F( G) Gauss-Bonnet gravity and also for F( T) gravity and we discuss the viability of each scenario by comparing the resulting spectral index with the latest observational data. [ABSTRACT FROM AUTHOR]

The Buchdahl limit for static spherically symmetric isotropic stars is generalised to the case of five dimensional Gauss-Bonnet gravity. Our result depends on the sign of the Gauss-Bonnet coupling constant $$\alpha $$ . When $$\alpha >0$$ , we find, unlike in general relativity, that the bound is dependent on the stellar structure, in particular the central energy density and we find that stable stellar structures can exist arbitrarily close to the black hole horizon. Thus stable stars can exist with extra mass in this theory compared to five dimensional general relativity. For $$\alpha <0$$ it is found that the Buchdahl bound is more restrictive than the general relativistic case. [ABSTRACT FROM AUTHOR]

We study the effect of higher-derivative terms on holographic Schwinger effect by introducing the Gauss-Bonnet term in the gravity sector. Anti-de Sitter soliton background is considered which is dual to confining phase of the boundary field theory. By calculating the potential between the produced pair, we find that larger Gauss-Bonnet factor $$\lambda $$ makes the pair lighter. We apply numerical method to calculate the production rate for various cases. The results show that the Gauss-Bonnet term enhances the production rate. The critical behaviors near the two critical values of the electric field are also investigated, and it is found that the two critical indexes are not affected by the Gauss-Bonnet term and thus suggests a possible universality. [ABSTRACT FROM AUTHOR]

In this paper, we consider quadratic Maxwell invariant as a correction to the Maxwell theory and study thermodynamic behavior of the black holes in Einstein and Gauss-Bonnet gravities. We consider cosmological constant as a thermodynamic pressure to extend phase space. Next, we obtain critical values in case of variation of nonlinearity and Gauss-Bonnet parameters. Although the general thermodynamical behavior of the black hole solutions is the same as usual Van der Waals system, we show that in special case of the nonlinear electromagnetic field, there will be a turning point for the phase diagrams and usual Van der Waals is not observed. This theory of nonlinear electromagnetic field provides two critical horizon radii. We show that this unusual behavior of phase diagrams is due to existence of second critical horizon radius. It will be pointed out that the power of the gravity and nonlinearity of the matter field modify the critical values. We generalize the study by considering the effects of dimensionality on critical values and make comparisons between our models with their special sub-classes. In addition, we examine the possibility of the existence of the reentrant phase transitions through two different methods. [ABSTRACT FROM AUTHOR]