Gauss-Bonnet Gravity Research Articles

Freedom near lightcone and ANEC saturation

Averaged Null Energy Conditions (ANECs) hold in unitary quantum field theories. In conformal field theories, ANECs in states created by the application of the stress tensor to the vacuum lead to three constraints on the stress-tensor three-point couplings, depending on the choice of polarization. The same constraints follow from considering two-point functions of the stress tensor in a thermal state and focusing on the contribution of the stress tensor in the operator product expansion (OPE). One can observe this in holographic Gauss-Bonnet gravity, where ANEC saturation coincides with the appearance of superluminal signal propagation in thermal states. We show that, when this happens, the corresponding generalizations of ANECs for higher-spin multi-stress tensor operators with minimal twist are saturated as well and all contributions from such operators to the thermal two-point functions vanish in the lightcone limit. This leads to a special near-lightcone behavior of the thermal stress-tensor correlators — they take the vacuum form, independent of temperature.

Thermal geometries and the Joule–Thomson expansion of modified charged and slowly rotating black holes

Thermodynamics of charged and slowly rotating black holes in 4D Gauss–Bonnet gravity has attracted a great deal of attention due to its intrinsic complications and rich phase structures. In this paper, we revisit the thermodynamics of charged and slowly rotating black holes and provide the correct thermodynamic volume and entropy. Thermodynamic geometries are a powerful tool to study the microstructure of black holes. Based on the Hessian matrix of the black hole mass, we introduce thermodynamic geometric methods and give its scalar curvature (Ruppeiner and Weinhold). Furthermore, we investigate the Joule–Thomson expansion of slowly rotating black hole in 4D Gauss–Bonnet gravity in this research study. Interestingly, we explicitly state that the expression of the Joule–Thomson coefficient is obtained from the basic formulas of enthalpy and temperature. Then, we obtain the isenthalpic curve in the T − P graph and demonstrate the cooling–heating region by the inversion curve. The inversion temperature and inversion curves are obtained, and we investigate the similarities and differences between van der Waals fluids and charged fluids.

A case study of small field inflationary dynamics in the Einstein–Gauss–Bonnet framework in the light of GW170817

We study two of the most theoretically promising models of inflation, namely Natural inflation and Mutated Hilltop inflation, in the Einstein-Gauss Bonnet(EGB) gravity framework. In this work, we try to explore these models keeping observations from GW170817 on the speed of gravitational wave to be equal to the speed of light. This has direct implications on the non-minimal coupling to the Gauss–Bonnet invariant in the action. Thus, the effective potential gets new features. We have not only analysed the inflationary dynamics, but also the reheating dynamics and finally the corresponding energy spectrum of the gravitational wave.

Power spectra of slow-roll inflation in the consistent D → 4 Einstein-Gauss-Bonnet gravity

The slow-roll inflation which took place at extremely high energy regimes is in general believed to be sensitive to the high-order curvature corrections to the classical general relativity (GR). In this paper, we study the effects of the high-order curvature term, the Gauss-Bonnet (GB) term, on the primordial scalar and tensor spectra of the slow-roll inflation in the consistent D → 4 Einstein Gauss-Bonnet (4EGB) gravity. The GB term is incorporated into gravitational dynamics via the re-scaling of the GB coupling constant α → α/(D-4) in the limit D → 4. For our purpose, we calculate explicitly the primordial scalar and tensor power spectra with GB corrections accurate to the next-to-leading order in the slow-roll approximation in the slow-roll inflation by using the third-order uniform asymptotic approximation method. The corresponding spectral indices and their runnings of the spectral indices for both the scalar and tensor perturbations as well as the ratio between the scalar and tensor spectra are also calculated up to the next-to-leading order in the slow-roll expansions. These results represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with Planck 2018 constraint in a model with power-law potential, we show that the second-order corrections are important in future measurements.

Charged fluids in higher order gravity

We generate the field equations for a charged gravitating perfect fluid in Einstein–Gauss–Bonnet gravity for all spacetime dimensions. The spacetime is static and spherically symmetric which gives rise to the charged condition of pressure isotropy that is an Abel differential equation of the second kind. We show that this equation can be reduced to a canonical differential equation that is first order and nonlinear in nature, in higher dimensions. The canonical form admits an exact solution generating algorithm, yielding implicit solutions in general, by choosing one of the potentials and the electromagnetic field. An exact solution to the canonical equation is found that reduces to the neutral model found earlier. In addition, three new classes of solutions arise without specifying the gravitational potentials and the electromagnetic field; instead constraints are placed on the canonical differential equation. This is due to the fact that the presence of the electromagnetic field allows for a greater degree of freedom, and there is no correspondence with neutral matter. Other classes of exact solutions are presented in terms of elementary and special functions (the Heun confluent functions) when the canonical form cannot be applied.

De Sitter potential in six dimensional Einstein–Gauss–Bonnet isotropic fluids

We present a physically reasonable stellar model in 6-dimensional Einstein–Gauss–Bonnet gravity by prescribing the de Sitter temporal metric potential. The model displays the necessary qualitative features of a compact star model with variable density profile. For a specified parameter space, the model is shown to be well-behaved in the sense that the energy density and pressure are both positive and smooth decreasing functions, with the pressure vanishing on a suitable hyper-surface, thus establishing a finite boundary for the isotropic distribution. Additionally, the model is causal, the energy conditions and adiabatic stability index are all satisfied. The exact solution does not contain the Einstein gravity model by switching off the higher curvature coupling. The model in the standard theory is constructed from the field equations, and its own associated parameter space is determined. The Einstein model displays some undesirable traits, which are eliminated when the higher curvature terms are active.

Quasibound States, Stability and Wave Functions of the Test Fields in the Consistent 4D Einstein–Gauss–Bonnet Gravity

We examine the interaction between quantum test particles and the gravitational field generated by a black hole solution that was recently obtained in the consistent 4-dimensional Einstein–Gauss–Bonnet gravity. While quasinormal modes of scalar, electromagnetic, and Dirac fields have been recently studied in this theory, there is no such study for the quasibound states. Here, we calculate the spectrum of quasibound states for the test fields in a spherically symmetric and asymptotically flat black hole solution in the consistent 4-dimensional Einstein–Gauss–Bonnet gravity. The quasispectrum of resonant frequencies is obtained by using the polynomial condition associated to the general Heun functions. We also discuss the stability of the systems for some values of the Gauss-Bonnet coupling constant.

Electromagnetic quasinormal modes of dyonic AdS black holes with quasitopological electromagnetism in a Horndeski gravity theory mimicking EGB gravity at D → 4

We investigate some properties of a black hole in a Horndeski gravity theory mimicking EGB gravity at [Formula: see text]. Borrowing ideas from quasitopological gravities provide a matter source of dyonic fields, in which the black hole solution carries two charges, electric and magnetic, in the context of the Einstein–Gauss–Bonnet (EGB) gravity. However, due to several limitations of the EGB gravity in [Formula: see text], we consider a Horndeski gravity theory which can mimic EGB gravity in [Formula: see text]. The essential practice used in this paper is the electromagnetic quasinormal modes process, with the goal of discovering the spectrum of such an electromagnetic perturbation over the black hole spacetime. The Wentzel–Kramer–Brillouin (WKB) approximation is used to achieve the desired results. The study shows that both the charges have similar impacts on the quasinormal modes.

Global monopoles in the extended Gauss-Bonnet gravity

We discuss self-gravitating global O(3) monopole solutions associated with the spontaneous breaking of O(3) down to a global O(2) in an extended Gauss-Bonnet theory of gravity in ($3+1$) dimensions, in the presence of a nontrivial scalar field $\mathrm{\ensuremath{\Phi}}$ that couples to the Gauss-Bonnet higher curvature combination with a coupling parameter $\ensuremath{\alpha}$. We obtain a range of values for $\ensuremath{\alpha}<0$ (in our notation and conventions), which are such that a global (Israel type) matching is possible of the space-time exterior to the monopole core $\ensuremath{\delta}$ with a de Sitter interior, guaranteeing the positivity of the Arnowitt-Deser-Misner (ADM) mass of the monopole, which, together with a positive core radius $\ensuremath{\delta}>0$, are both dynamically determined as a result of this matching. It should be stressed that in the general relativity (GR) limit, where $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, and $\mathrm{\ensuremath{\Phi}}\ensuremath{\rightarrow}\text{constant}$, such a matching yields a negative ADM monopole mass, which might be related to the stability issues the [Barriola-Vilenkin (BV)] global monopole of GR faces. Thus, our global monopole solution, which shares many features with the BV monopole, such as an asymptotic-space-time deficit angle, of potential phenomenological/cosmological interest, but has, par contrast, a positive ADM mass, has a chance of being a stable configuration, although a detailed stability analysis is pending.

Five-dimensional cylindrical anisotropic fluid in Einstein–Gauss–Bonnet gravity

In this paper, we present a static solution for the five-dimensional Einstein–Gauss–Bonnet (EGB) gravitational field equations with a cylindrical symmetry and an anisotropic fluid as a source. We consider whole set of equations in the interior space which sourced by static cylindrical anisotropic fluid and junction conditions required for smoothly matching with exterior space which is a cylindrical vacuum solution of five dimensional EGB equation. We achieve density and pressures as functions of cylindrical radial coordinate and give some graphically analysis under numerical solution.

On heat properties of charged AdS black holes in Gauss-Bonnet gravity coupled with nonlinear electrodynamics

We investigate the heat properties of charged AdS black holes in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics. We consider the thermodynamics of black holes from the perspective of heat capacity and show that the nonlinear electrodynamics can be helpful to improve the thermodynamic stability of black holes. We perform a two-dimensional description in order to reproduce the Hawking temperature, which confirms that the Hawking temperature has an intrinsic topological nature and holds for a higher dimensional spherically symmetric spacetime. We also analyze the Maxwell equal area law and coexistence curve, and find the existence of van der Waals-like phase transitions based on critical exponents. Moreover, we deal with a charged AdS black hole in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics as a working material to study holographic heat engines and obtain an exact expression for the efficiency of a rectangular engine cycle. We then discuss the effects of nonlinear electrodynamics and Gauss-Bonnet couplings on the rectangular engine cycle and compare the efficiency of this cycle with that of the Carnot cycle.

Inflationary dynamics and swampland criteria for modified Gauss-Bonnet gravity compatible with GW170817

In this article we present an alternative formalism for the inflationary phenomenology of rescaled Einstein-Gauss-Bonnet models which are in agreement with the GW170817 event. By constraining the propagation velocity of primordial tensor perturbations, an approximate form for the time derivative of the scalar field coupled to the Gauss-Bonnet density is extracted. In turn, the overall degrees of freedom decrease and similar to the case of the canonical scalar field, only one scalar function needs to be designated, while the other is extracted from the continuity equation of the scalar field. We showcase explicitly that the slow-roll indices can be written in a closed form as functions of three dimensionless parameters, namely $x=\frac{1}{2\alpha}\bigg(\frac{\kappa\xi'}{\xi''}\bigg)^2$, $\beta=8H^2\xi''$ and $\gamma=\frac{\xi'\xi'''}{\xi''^2}$ and in turn, we prove that the Einstein-Gauss-Bonnet model can in fact produce a blue-tilted tensor spectral index if the condition $\beta\geq1$ is satisfied, which is possible only for Einstein-Gauss-Bonnet models with $\xi''(\phi_k)>0$. Afterwards, a brief comment on the running of the spectral indices is made where it is shown that $a_{\mathcal{S}}(k_*)$ and $a_{\mathcal{T}}(k_*)$ in the constrained case are approximately of the order $\mathcal{O}(10^{-3})$, if not smaller. Last but not least, we examine the conditions under which the Swampland criteria are satisfied. We connect the tracking condition related to scalar field theories with the present models, and we highlight the important feature of the models we propose that the tracking condition can be satisfied only if the Swampland criteria are simultaneously satisfied, however the cases with $\xi\sim1/V$ and $\xi\sim V$ are excluded, as they cannot describe the inflationary era properly.

Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity

This work provides the exact solution of the Bardeen black hole in association with [Formula: see text] Gauss–Bonnet massive gravity in Anti-de-Sitter [Formula: see text] 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 [Formula: see text] EGB Bardeen black holes when the massive gravity parameter is set to zero and it yields a [Formula: see text] Gauss–Bonnet black hole in the absence of magnetic monopole charge. Further, we analyze and adopt the thermodynamic quantities like mass ([Formula: see text]), temperature [Formula: see text] and heat capacity [Formula: see text] in the presence of massive gravity and nonlinear electrodynamics. In addition, we extend our results by considering the cosmological constant [Formula: see text] as a thermodynamical variable [Formula: see text] and obtain the critical values of pressure, temperature, horizon radius and analyze the behavior of the global parameter [Formula: see text]. The effect of a massive parameter ([Formula: see text]) of the critical exponent is opposite to the magnetic monopole charge ([Formula: see text]) and Gauss–Bonnet parameter ([Formula: see text]). 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.

Quasinormal modes of extended gravity black holes through higher order WKB method

Black hole’s quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the spectrum of the quasinormal modes of Hayward black hole in Einstein–Gauss–Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein–Lovelock gravity. By utilizing the 6th-order WKB resonance technique, we examine the quasinormal modes frequencies [Formula: see text] by shifting the charge parameter [Formula: see text] (it is also identified with the cosmological constant), circular harmonic index [Formula: see text], and mass of scalar field [Formula: see text]. We observe that 6th-order WKB method gives quite high accuracy when the multipole number [Formula: see text] is larger than the overtone [Formula: see text]. We observe that real and imaginary components of the quasinormal modes are not linear functions similar to Reisnner–Nordström-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

Phases of Rotating Black Objects in d = 5 Einstein–Gauss–Bonnet Theory

We considered several different classes of asymptotically flat, rotating black objects in d=5 Einstein–Gauss–Bonnet (EGB) theory. These are black holes with two equal-magnitude angular momenta, in which case extremal configurations are studied as well. Numerical evidence is also given for the existence of EGB generalizations of the Myers–Perry black holes with a single plane of rotation and of the Emparan–Reall balanced black rings. All solutions approach asymptotically the Minkowski background and present no singularities outside or on the horizon. The numerical results suggest that, for any mass of the solutions and any topology of the horizon, the rotating configurations exist up to a maximal value of the GB coupling constant, while the solutions with a spherical horizon topology still satisfy the Einstein gravity bound on angular momentum.

Dynamical analysis in regularized 4D Einstein–Gauss–Bonnet gravity with non-minimal coupling

We investigate the regularized four-dimensional Einstein–Gauss–Bonnet (4DEGB) gravity with a non-minimal scalar coupling function, which is an extension of the regularized 4DEGB theory. By introducing non-minimal coupling to the Gauss-Bonnet term, we demonstrate the additional contribution to the dynamical equations which is otherwise absent in the dimensionally regularized theory. Furthermore, we analyze the stability of the system by using the dynamical system approach based on fixed points. Then, we consider time evolution to investigate the history of the universe and to constrain observational data to obtain the cosmological parameters of the model.

Negative mass black holes in de Sitter space

We show that asymptotically de Sitter black holes of negative mass can exist in Lovelock gravity. Such black holes have horizon geometries with non-constant curvature and are known as Exotic Black Holes. We explicitly examine the case of Gauss-Bonnet gravity. We briefly discuss the positive mass case where we show how the transverse space geometry affects whether a black hole will exist or not.For negative mass solutions we shown how three different black hole spacetimes are possible depending on the transverse space geometry. We also provide closed form expressions for the geometric parameters to ensure that a black hole spacetime is observed. We close with a discussion of the massless case, where there are many different spacetimes that are permitted.

Evolution of gravitational radiation from black hole under the influence of Einstein–Gauss–Bonnet gravity

In our work, we compute the 4-dimensional Einstein–Gauss–Bonnet gravity black hole solution by applying the Newman–Janis approach and also examine the Hawking temperature. The generalized uncertainty principle (GUP) is applied to compute the Lagrangian field equation and by using the semi-classical phenomenon, we analyze the modified Hawking temperature. By taking into account the graphical analysis, we check the stable conditions of the black hole with the influence of rotation parameter, charged parameter and quantum gravity parameter. Furthermore, we compute the logarithmic entropy corrections in the background of corrected temperature and standard entropy for corresponding black hole. We study the behavior of different thermodynamics quantities like Helmholtz free energy, internal energy, Gibbs free energy and heat capacity under these fluctuations. In our analysis, we note that these corrections enhance the stability of this system, so, under the effects of these corrections, the considered geometry becomes more stable.

On the gravitational collapse in 4-dimensional Einstein–Gauss–Bonnet gravity

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.

Bouncing behaviours in four dimensional Einstein Gauss-Bonnet gravity with cosmography and observational constraints

Bouncing behaviours in four dimensional Einstein Gauss-Bonnet gravity with cosmography and observational constraints