Based on the shooting method, we numerically investigate the properties of holographic paramagnetism-ferromagnetism phase transition in the presence of higher order Gauss-Bonnet (\emph{GB}) correction terms on the gravity side. On the matter field side, however, we consider the effects of the Power-Maxwell (\emph{PM}) nonlinear electrodynamics on the phase transition of this system. For this purpose, we introduce a massive $2-$form coupled to \emph{PM} field, and neglect the effects of $2-$form fields and gauge field on the background geometry. We observe that increasing the strength of both the power parameter $q$ and \emph{GB} coupling constant $α$ decrease the critical temperature of the holographic model, and lead to the harder formation of magnetic moment in the black hole background. Interestingly, we find out that at low temperatures, the spontaneous magnetization and ferromagnetic phase transition happen in the absence of external magnetic field. In this case, the critical exponent for magnetic moment has the mean field value, $1/2$, regardless of the values of $q$ and $α$. In the presence of external magnetic field, however, the magnetic susceptibility satisfies the Curie-Weiss law.
We compute the second order transport coefficients of a hydrodynamic theory with Einstein-Gauss-Bonnet gravity dual. We show the breakdown of the universal hydrodynamic relation $ -2 λ_0 + 4 λ_1 - λ_2 = 0 $ for the general values of the Gauss-Bonnet coupling.
With in the extended thermodynamics, we give a comparative study of critical heat engines for Gauss-Bonnet and charged black holes in AdS in five dimensions, in the limit of large Gauss-Bonnet parameter $α$ and charge $q$, respectively. We show that the approach of efficiency of heat engines to Carnot limit in Gauss-Bonnet black holes is higher(lower) than charged black holes when corresponding parameters are small(large).
The Gauss-Bonnet interaction is the only consistent quadratic interaction below the Planck scale in the Randall-Sundrum compactification. We study various static and inflationary solutions including this Gauss-Bonnet interaction.
We study the emission of gravitons by a homogeneous brane with the Gauss-Bonnet term into an Anti de Sitter five dimensional bulk spacetime. It is found that the graviton emission depends on the curvature scale and the Gauss-Bonnnet coupling and that the amount of emission generally decreases. Therefore nucleosynthesis constraints are easier to satisfy by including the Gauss-Bonnet term.
We study the effect of the Gauss-Bonnet term on vacuum decay process in the Coleman-De Luccia formalism. The Gauss-Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss-Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss-Bonnet coefficient.
In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless $SU(2)$ gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Ga…
Rotating charged Gauss-Bonnet black hole solutions in higher dimensional ($d >4$), asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit. The angular momentum, magnetic dipole moment, and the gyromagnetic ratio of the black holes are calculated and it turns out that the Gauss-Bonnet term does not affect to the gyromagnetic ratio.
A black brane solution to a Gauss-Bonnet massive gravity is introduced. In the context of AdS/CFT correspondence, the viscosity to entropy ratio is found by the Green-Kubo formula. The result indicates violation of the well-known KSS bound as expected in a higher derivative theory. Setting mass zero gives back the known viscosity to entropy ratio dependent on the Gauss-Bonnet coupling, while without Gauss-Bonnet term, a nonzero mass parameter doesn't contribute to the ratio which saturates the bound of $1/4π$.
Assuming $ω=\sum_n C^{(n)}q^{2n}$ in the low-frequency limit, we apply the refined recipe to compute the dispersion relation of shear quasinormal modes of the Gauss-Bonnet black brane. Treating the Gauss-Bonnet parameter $\lagb$ nonperturbatively and the momentum $q$ perturbatively, we work out $C^{(1)}$, $C^{(2)}$, confirm previous results in the literature and pave the way to a general formula for $C^{(n)}$.
We compute all the second order transport coefficients of a hydrodynamic theory with a gravity dual which includes a Gauss-Bonnet term. We find that a particular linear combination of the second order transport coefficients, which was found to vanish in generic two derivative gravity theories with matter, remains zero even in the presence of the Gauss-Bonnet term. We contrast this behavior with the shear viscosity to entropy density ratio.
We consider a "Scalar-Einstein-Gauss-Bonnet" theory in four dimension, where the scalar field couples non minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from exterior by an apparent horizon.
We study the holographic p-wave superconductors in a five-dimensional Gauss-Bonnet gravity with an SU(2) Yang-Mills gauge field. In the probe approximation, we find that when the Gauss-Bonnet coefficient grows, the condensation of the vector field becomes harder, both the perpendicular and parallel components, with respect to the direction of the condensation, of the anisotropic conductivity decrease. We also study the mass of the quasi-particle excitations, the gap frequency and the DC conductivities of the p-wave superconductor. All of them depend on the Gauss-Bonnet coefficient. In addition…
Configurational entropy has been revealed as a reliable method for constraining some parameters of a given model [Phys. Rev. D \textbf{92} (2015) 126005, Eur. Phys. J. C \textbf{76} (2016) 100]. In this letter we calculate the configurational entropy in Gauss-Bonnet braneworld models. Our results restrict the range of acceptability of the Gauss-Bonnet scalar values. In this way, the information theoretical measure in Gauss-Bonnet scenarios opens a new window to probe situations where the additional parameters, responsible for the Gauss-Bonnet sector, are arbitrary. We also show that such an ap…
We investigate the thermodynamics of confnement/deconfinement transition in soft wall model of QCD with Gauss-Bonnet corrections using AdS/CFT correspondence. In bulk AdS space-time the transition is geometric and is known as Hawking-Page transition. The Hawking-Page transition be- tween two geometries, namely charged AdS black hole and thermally charged AdS have been studied with Gauss-Bonnet corrections up-to first order. The Gauss-Bonnet coupling modifies the transition temperature of the system, but qualitative features remain unchanged. We obtain the curves between chemical potential and …
We show that the Gauss-Bonnet term is the only consistent curvature squared interaction in the Randall-Sundrum model and various static and inflationary solutions can be found. And from metric perturbations around the RS background with a single brane embedded, we also show that for a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the 4D Einstein gravity at the linearized level.
We study anisotropic inflation with Gauss-Bonnet correction in presence of a massless vector field. In this scenario, exact anisotropic power-law inflation is realized when the inflaton potential, gauge coupling function and the Gauss-Bonnet coupling are exponential functions. We show that anisotropy becomes proportional to two slow-roll parameters of the theory and hence gets enhanced in presence of quadratic curvature corrections. The stability analysis reveals that anisotropic power-law solutions remain stable over a substantially large parameter region.
We examine the relativistic Nambu-Goto model with Gauss-Bonnet boundary term added to the action integral. The system is analysed using an invariant representation of dynamical string degrees of freedom by complex Liouville fields. The solutions of classical equations of motion for open strings are described.
The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein-Gauss-Bonnet black holes.
I review recent work on holographic superconductivity with Einstein-Gauss-Bonnet gravity, and show how the critical temperature of the superconductor depends on both gravitational backreaction and the Gauss-Bonnet parameter, using both analytic and numerical arguments. I also review computations of the conductivity, finding the energy gap, and demonstrating that there is no universal gap ratio, $ω_g/T_c$, for these superconductors.
The phase transition of the Gauss-Bonnet AdS black hole has the similar property with the van der Waals thermodynamic system. However, it is determined by the Gauss-Bonnet coefficient α, not only the horizon radius. Furthermore, the phase transition is not the pure one between a big black hole and a small black hole. With this issue, we introduce a new order parameter to investigate the critical phenomenonand to give the microstructure explanation of the Gauss-Bonnet AdS black hole phase transition. And the critical exponents are also obtained. At the critical pointof the Gauss-Bonnet AdS blac…
The effective four-dimensional, linearised gravity of a Randall-Sundrum-like brane world model is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a scalar field. The resulting brane worlds can have better agreement with observations than the equivalent Einstein gravity models.
We consider the effective action of M-theory compactified on a S^1/Z_2 orbifold with R^2 interaction in the Gauss-Bonnet combination. We derive equations of motion with source terms arising from the Gauss-Bonnet terms and find the M2-brane solution up to order κ^{2/3}. It receives a correction which depends on the orbifold coordinate in the same form as the gauge 5-brane solution.
We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space, by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form exp(Delta S) where S is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitt…
We investigate nonperturbative dilatonic solutions of the wide class of the modified gravity models including the Gauss-Bonnet terms with a general $F(G)$ Lagrangian. We show that presence of the Liouville-like solutions is a characteristic feature of these models.
This is a report of our recent investigation on the extremal dilatonic black holes in four dimensional Gauss-Bonnet gravity. We found that a global solution can exist only when the dilaton coupling is less than a critical value which can be determined numerically. Moreover, the black hole horizon is stretched by the Gauss-Bonnet correction and the entropy is twice the value given by Bekenstein-Hawking formula.
In this work we deal with the presence of braneworld solutions in a five-dimensional space-time with a single extra spatial dimension of infinite extent. The braneworld scenario is built under the presence of a single real scalar field, and we modify the gravity sector to include generic function of the Gauss-Bonnet term. We study several specific models, and we construct exact braneworld solutions, in particular for including the Gauss-Bonnet term at first and second order power. As an interesting result, we show that the brane tends to split for a specific modification in the gravity sector,…
We obtain the full 5D graviton propagator in the Randall-Sundrum model with the Gauss-Bonnet interaction. From the decomposition of the graviton propagator on the brane, we show that localization of gravity arises in the presence of the Gauss-Bonnet term. We also obtain the metric perturbation for observers on the brane with considering the brane bending and compute the amplitude of one massless graviton exchange. For the positive definite amplitude or no ghost states, the sign of the Gauss-Bonnet coefficient should be negative in our convention, which is compatible with string amplitude compu…
We prove that in anti de Sitter space, there is no van Dam-Veltman-Zakharov discontinuity in the graviton propagator. Here we obtain the mass term of $M^2\propto Λ^2$ from the Gauss-Bonnet term, which is a ghost-free one. The condition that the massless limit is smooth is automatically satisfied for this case.
We investigate deformations of Gauss-Bonnet-Lifshitz holography in $(n+1)$ dimensional spacetime. Marginally relevant operators are dynamically generated by a momentum scale $Λ\sim 0$ and correspond to slightly deformed Gauss-Bonnet-Lifshitz spacetimes via a holographic picture. To admit (non-trivial) sub-leading orders of the asymptotic solution for the marginal mode, we find that the value of the dynamical critical exponent $z$ is restricted by $z= n-1-2(n-2) \tildeα$, where $\tildeα$ is the (rescaled) Gauss-Bonnet coupling constant. The generic black hole solution, which is characterized by…
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.
We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The construction allows to deal with a general background and includes the Gibbons-Hawking-Myers boundary term as a special case, when the background is tak…
We derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term. Using the modified Lichnerowicz equation we study the metric perturbations of Gauss-Bonnet black strings in Codimension-2 Braneworlds.
To ensure the existence of a well defined linearized gravitational wave equation, we show that the spacetimes in the so-called "Einstein-Gauss-Bonnet gravity in four dimension" have to be locally conformally flat.
We discuss a new extended gravity model in ordinary $D=4$ spacetime dimensions, where an additional term in the action involving Gauss-Bonnet topological density is included without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. Avoiding the Gauss-Bonnet density becoming a total derivative is achieved by employing the formalism of metric-independent non-Riemannian spacetime volume-forms. The non-Riemannian volume element triggers dynamically the Gauss-Bonnet scalar to become an arbitrary integration constant on-shell. We describe in some det…
Using Noether's identities, we define a superpotential with respect to a background for the Einstein Gauss-Bonnet theory of gravity. As an example, we show that its associated conserved charge yields the mass-energy of a D-dimensional Gauss-Bonnet black hole in an anti-de Sitter spacetime.
We study the bending of light in the space-time of black holes in four-dimensional Einstein-Gauss-Bonnet theory of gravity, recently proposed by Glavan and Lin \cite{Glavan}. Using Rindler-Ishak method, the effect of Gauss-Bonnet coupling on the bending angle is studied. We show that a positive Gauss-Bonnet coupling gives a negative contribution to the Schwarzschild-de Sitter deflection angle, as one would expect.
We study charged black hole solutions in 4-dimensional (4D) Einstein-Gauss-Bonnet-Maxwell theory to the linearized perturbation level. We first compute the shear viscosity to entropy density ratio. We then demonstrate how bulk causal structure analysis imposes a upper bound on the Gauss-Bonnet coupling constant in the AdS space. Causality constrains the value of Gauss-Bonnet coupling constant $α_{GB}$ to be bounded by $α_{GB}\leq 0$ as $D\rightarrow 4$.
In this paper we have analytically investigated holographic superconductors in four dimensional Einstein-Gauss-Bonnet gravity background. Recently the novel four dimensional Einstein-Gauss-Bonnet gravity has been formulated by rescaling the Gauss-Bonnet coupling constant $α\rightarrow \fracα{d-4}$ and taking the limit $d\rightarrow 4$, and this predicts several interesting new features. To know the effect of the curvature correction on the $(2+1)$-dimensional superconductors, we have consider the $3+1$-dimensional Einstein-Gauss-Bonnet gravity. Using the Sturm-Liouville eigenvalue approach, th…
Accelerating vacua with maximally symmetric, but not necessarily spherical, sections for Einstein and Gauss-Bonnet gravities in generic dimensions are obtained. The acceleration parameter has the effect of shifting the cosmological constants in Einstein gravity, whereas in Gauss-Bonnet gravity the effective cosmological constants remain the same in the presence of acceleration as in the case without acceleration.
It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $Λ$ and the Gauss-Bonnet coupling $α$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the…
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 discuss the formation of scalar hair on Gauss-Bonnet solitons and black holes in 5-dimensional Anti-de Sitter (AdS) space-time. We present new results on the static case and point out further details. We find that the presence of the Gauss-Bonnet term has an influence on the pattern of soliton solutions for small enough values of the electric charge. We also discuss rotating Gauss-Bonnet black holes with and without scalar hair.
We propose a new model of $D=4$ Gauss-Bonnet gravity. To avoid the usual property of the integral over the standard $D=4$ Gauss-Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D=4 Gauss-Bonnet action term non-trivial without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss-Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cos…
We construct generalizations of the D=5 Kerr black string by including higher curvature corrections to the gravity action in the form of the Gauss-Bonnet density. These uniform black strings satisfy a generalised Smarr relation and share the basic properties of the Einstein gravity solutions. However, they exist only up to a maximal value of the Gauss-Bonnet coupling constant, which depends on the solutions' mass and angular momentum.
We study the Wilson line response in the holographic superconducting phase transitions in Gauss-Bonnet gravity. In the black brane background case, the Little-Parks periodicity is independent of the Gauss-Bonnet parameter, while in the AdS soliton case, there is no evidence for the Little-Parks periodicity. We further study the impact of the Gauss-Bonnet term on the holographic phase transitions quantitatively. The results show that such quantum corrections can effectively affect the occurrence of the phase transitions and the response to the Wilson line.
The Kerr-type solutions of the five-dimensional Einstein and Einstein-Gauss-Bonnet equations look pretty similar when written in Kerr-Schild form. However the Myers-Perry spacetime is circular whereas the rotating solution of the Einstein-Gauss-Bonnet theory is not. We explore some consequences of this difference in particular regarding the (non) existence of Boyer-Lindquist-type coordinates and the extension of the manifold.
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from standard Noether identities. The calculation relies on the fact that the Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when linearized on maximally symmetric backgrounds and uses the recently discovered D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations.
We treat spherically symmetric black holes in Gauss-Bonnet gravity by imposing boundary conditions on fluctuating metric on the horizon. Obtained effective two-dimensional theory admits Virasoro algebra near the horizon. This enables, with the help of Cardy formula, evaluation of the number of states. Obtained results coincide with the known macroscopic expression for the entropy of black holes in Gauss-Bonnet gravity.
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.
We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol…
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black hole's background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increase…
We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and non-minimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the non-minimally coupling constant, the spacetime dimension, the cosmological constant and the Gauss-Bonnet coefficient in detail. We find that the non-minimal coupling may suppress the Hawking radiation, while the Gauss-Bonnet coupl…
It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant. We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions. Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter. One branch (the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero, in which case the…
In this paper we consider the holographic DC and Hall conductivity in Einstein-Maxwell-Dilaton in Gauss-Bonnet gravity with momentum dissipation. We analytically derived the DC conductivity and Hall conductivity from the black horizon data, and found that the conductivities are independent on the Gauss-Bonnet coupling. We also used the entropy function formalism to get the conductivities in terms of the charge of the black hole, even without knowing the explicit black hole solutions.
We study general models for holographic superconductors in Einstein-Gauss-Bonnet gravity. We find that different values of Gauss-Bonnet correction term and model parameters can determine the order of phase transitions and critical exponents of second-order phase transitions. Moreover we find that the size and strength of the conductivity coherence peak can be controlled. The ratios $ω_g/Tc$ for various model parameters have also been examined.
We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multi-poles $\ell$ and large Gauss-Bonnet coupling $α$ for $D= 5, 6$, which is stabilized at higher $D$. Although small negative gap of the effective potential for scalar type of gravitational perturbations, exists for higher $D$ and whatever $α$, it does not lead to any instability.
We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given in both the metric and the first order formalisms.
