Gauss-Bonnet Gravity Research Articles

Dynamical systems of modified Gauss–Bonnet gravity: cosmological implications

In this paper, we derive the field equations of modified Gauss–Bonnet gravity termed as f(R, G) gravity for the non-flat Friedmann–Robertson–Walker (FRW) spacetime. We utilize the dynamical system approach to study the cosmic dynamics of two different class of f(R, G) models composed of radiation and matter (cold dark matter and baryonic matter). The linear perturbations around the fixed points are studied to explore the corresponding stability of points. The cosmological implications are studied in f(R,G)=f0RnG1-n and f(R,G)=f0Rα+f1Gβ models to identify the qualitative evolution of universe with the flat-FRW spacetime. The qualitative differences between the considered class of models are discussed in detail. The fixed points corresponding to the late-time accelerated and radiation phase of the universe will exist in the model but, the existence of fixed point corresponding to the matter dominated phase will depend on the functional form of f(R, G). Furthermore, the autonomous systems are utilized to study the cosmographic parameters along with the statefinder diagnostic.

Islands on codim-2 branes in Gauss-Bonnet Gravity

Abstract We study the black hole information problem on codim-2 branes in Gauss-Bonnet gravity.
Thanks to the island surface ending on the brane, the Page curve of eternal black holes can
be recovered for all of the GB couplings within the causal constraints. Our results strongly
support the universality of the island mechanism. Similar to Einstein’s gravity, the HM surface
can exist only in a finite time in GB gravity. Remarkably, for various parameters, the maximum
times of HM surface are always larger than the Page times. As a result, the strange behavior of
HM surfaces does not affect the Page curves for general GB gravity. Finally, we establish the
correlation between the Page time, GB couplings, and brane tension, revealing that the Page
time increases with these factors.

The impact of modified gauss-bonnet gravity on a shear-free axial system

The impact of modified gauss-bonnet gravity on a shear-free axial system

Thermodynamic aspects of higher-dimensional black holes in Einstein–Gauss–Bonnet gravity through exponential entropy

Abstract We assume exponential corrections to the entropy of $5D$ charged AdS
black hole solutions, which are derived within the framework of
Einstein Gauss-Bonnet gravity and nonlinear electrodynamics.
Additionally, we consider two distinct versions of $5D$ charged AdS
black holes by setting the parameters $q\rightarrow0$ and
$k\rightarrow0$ (where $q$ represents charge, $k$ is the non-linear
parameter). We investigate these black holes in the extended phase
space, where the cosmological constant is interpreted as pressure,
and demonstrate the first law of black hole thermodynamics. The
focus extends to understanding the thermal stability or instability,
as well as identifying first and second-order phase transitions.
This exploration is carried out through the analysis of various
thermodynamic quantities, including heat capacity at constant
pressure, Gibbs free energy, Helmholtz free energy, and the trace of
the Hessian matrix. In order to visualize phase transitions,
identify critical points, analyzing stability and provide
comprehensive analysis, we have made the contour plot of the
mentioned thermodynamic quantities and observed that our results are
very much consistent. These investigations are conducted within the
context of exponentially corrected entropies, providing valuable
insights into the intricate thermodynamic behavior of these $5D$
charged AdS black holes under different parameter limits.

The Chini integrability condition in second order Lovelock gravity

We analyse neutral and charged matter distributions in second order Lovelock gravity, also known as Einstein–Gauss–Bonnet gravity, in arbitrary dimensions for a static, spherically symmetric spacetime. We first transform the charged condition of pressure isotropy, an Abel differential equation of the second kind, into canonical form. We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. This enables us to find three new general solutions, in implicit form, to the condition of pressure isotropy. We also show that previously obtained exact specific solutions arise as special cases in our general class of models. The Chini invariant does not arise in general relativity; it is a distinguishing feature of Einstein–Gauss–Bonnet gravity.

Energy conditions in Gauss–Bonnet gravity

We study the Energy Conditions in modified f(G) gravity, with G being the topological Gauss–Bonnet term. Then we use the cosmographic parameters to constrain the functional form of the gravitational action and investigate the possibility to have standard inflation in the early time. Specifically, we select models containing symmetries within the modified f(G) theory and obtain conditions for which (i) the energy conditions can be violated and (ii) the magnitude of the slow-roll parameters is small, thus suggesting that under given limits the analyzed theory can potentially trace the cosmic history both at early and at the late times.

Topological classification of critical points for hairy black holes in Lovelock gravity

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, T=T(V,xi), as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Power law cosmology in Gauss-Bonnet gravity with pragmatic analysis

In this study, we present an approach f(R,G) gravity incorporating power law in G. To study the cosmic evolution of the universe given by the reconstruction of the Hubble parameter given by E(z)=(1+z(α+(1+z)β)2β+1)32β. Subsequently, we use various recent observational datasets of OHD, Pantheon, and BAO to estimate the model parameters H0,α, and β applying the Markov Chain Monte Carlo (MCMC) technique in the emcee package to establish the validity of the model. In our findings, we observe that our model shows consistency with standard ΛCDM, transits from deceleration to acceleration, and enters the quintessence region in late times. The cosmological model satisfies necessary energy constraints, simultaneously violating the strong energy condition (SEC), indicating a repulsive nature and consistent with accelerated expansion. The cosmic evolution of the Hawking temperature and the total entropy for the various observational datasets also show the validity of the model. Thus, our established model demonstrates sufficient potential for explicitly describing cosmological models.

Inflationary dynamics of Mutated Hilltop inflation in Einstein–Gauss–Bonnet Gravity under new slow-roll approximations with generalized reheating

The advancement in the observational cosmology of the early universe such as Cosmic Microwave Background (CMB) observations, puts severe constraints on the inflationary models. Many inflationary models have been ruled out by CMB, nevertheless the models ruled out in standard cold inflationary scenarios can be resurrected in modified gravity models. In this regard we examine the dynamics of inflation within the framework of Einstein–Gauss–Bonnet (EGB) Gravity using the new slow-roll approximation methods proposed in Pozdeeva et al. (2024). We consider the Mutated Hilltop inflation model (Pal et al., 2010; Pinhero and Pal, 2019) due to its origin from super-gravity, a naturally perfect choice to study the impact of EGB on inflationary observables such as tensor-to-scalar ratio (r) and scalar spectral index (ns). The period of reheating following the inflationary phase is also examined, and for the Planck’18 permitted values of ns, constraints on the reheating temperature (Tre) are computed for various equations of states during reheating (ωre).

A viable model of self-gravitating object in the 5D Einstein Gauss-Bonnet Gravity

A viable model of self-gravitating object in the 5D Einstein Gauss-Bonnet Gravity

The pseudospectrum and transient of Kaluza–Klein black holes in Einstein–Gauss–Bonnet gravity

Abstract The spectrum and dynamical instability, as well as the transient effect of the tensor perturbation for the so-called Maeda–Dadhich black hole, a type of Kaluza–Klein black hole, in Einstein–Gauss–Bonnet gravity have been investigated in framework of pseudospectrum. We cast the problem of solving quasinormal modes (QNMs) in AdS-like spacetime as the linear evolution problem of the non-normal operator in null slicing by using ingoing Eddington–Finkelstein coordinates. In terms of spectrum instability, based on the generalized eigenvalue problem, the QNM spectrum and ε-pseudospectrum has been studied, while the open structure of ε-pseudospectrum caused by the non-normality of operator indicates the spectrum instability. In terms of dynamical instability, we introduce the concept of the distance to dynamical instability, which plays a crucial role in bridging the spectrum instability and the dynamical instability. We calculate such distance, named the complex stability radius, as parameters vary. Finally, we show the behavior of the energy norm of the evolution operator, which can be roughly reflected by the three kinds of abscissas in context of pseudospectrum, and find the transient growth of the energy norm of the evolution operator.

Gauss–Bonnet AdS planar and spherical black hole thermodynamics and holography

Abstract In this work, we extend the study in Bilic and Fabris (2022 J. High Energy Phys. JHEP11(2022)013) incorporating the AdS/CFT duality to establish a relationship between the local temperatures (Tolman temperatures) of a large (AdS) spherical and a (AdS) planar Schwarzschild black hole near the AdS boundary considering Gauss–Bonnet (GB) curvature correction in the gravitational action. We have shown that the higher curvature corrections appear in the local temperature relationship due to the inclusion of GB term in the bulk. By transforming the metric into Fefferman–Graham form, we have calculated the energy density of the conformal fluid at the boundary. The obtained result contains finite coupling corrections which are holographically induced by the GB curvature correction in the bulk theory. Following the well known approach of fluid/gravity duality, the energy density of the conformal fluid at the boundary is then compared with the black body radiation energy density. This comparison shows that the energy density is proportional to the temperature of the conformal fluid. The temperature of the conformal fluid is then shown to be related to the Tolman temperature of the black hole which then eventually helps us to establish both the Hawking temperature and Tolman temperature relationship between large spherically symmetric and planar Schwarzschild black holes in GB gravity near the AdS boundary.

Interacting models of dark energy and dark matter in Einstein scalar Gauss Bonnet gravity

We study the dynamics of the interacting models between the Gauss-Bonnet (GB) coupled scalar field and the dark matter fluid in a homogeneous and isotropic background. A key feature of GB coupling models is the varying speed of gravitational waves (GWs). We utilize recent constraints on the GW speed and conduct our analysis in two primary scenarios: model-dependent and model-independent. In the model-dependent scenario, where determining the GW speed requires a specific GB coupling functional form, we choose an exponential GB coupling. We adopt a dynamical system analysis to obtain the necessary constraints on the model parameters that describe different phases of the universe and produce a stable late-time accelerating solution following the GW constraint, and find that to satisfy all these constraints, fine-tuning of the free parameters involved in the models is often needed. In the model-independent scenario, the GW speed is fixed to one, and we construct the autonomous system to identify the late-time stable accelerating critical points. Furthermore, we adopt a Bayesian inference method using late-time observational data sets, including 31 data points from cosmic chronometer data (Hubble data) and 1701 data points from Pantheon+ and find that all the observational constraints can be satisfied without fine-tuning. In addition, we also utilize simulated binned Roman and LSST data to study the evolution of the universe in the model-independent scenario. We find that the model shows significant deviation at higher redshifts from ΛCDM and fits the current data much better than ΛCDM within the error bars.

Massive scalar clouds and black hole spacetimes in Gauss-Bonnet gravity

We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its Compton wavelength. We numerically compute sGB black hole spacetimes and scalar configurations and also compare with perturbative results for small couplings, where we focus on a dilatonic coupling function. We analyze the constraints on the parameters from requiring the curvature singularity to be located inside the black hole horizon r_hrh and the relation to the regularity condition for the scalar field. For scalar field masses m r_h \gtrsim 10^{-1}mrh≳10−1, this leads to a new and currently most stringent bound on sGB coupling constant \alphaα of \alpha/r_h^2\sim 10^{-1}α/rh2∼10−1 in the context of stellar mass black holes. Lastly, we look at several properties of the black hole configurations relevant for further work on observational consequences, including the scalar monopole charge, Arnowitt–Deser–Misner mass, curvature invariants and the frequencies of the innermost stable circular orbit and light ring.

Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields

In this paper, we investigate the time dependent black holes in the frame of Einstein–Gauss–Bonnet theory having two scalar fields and investigate the propagation of the gravitational wave (GW). In the reconstructed models, there often appear ghosts, which could be eliminated by imposing some constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss–Bonnet coupling during their propagation. The speed of propagation changes due to the coupling during the black hole formation process. The propagation speed of gravitational waves differs when they enter the black hole compared to when they exit.

Black holes, photon sphere, and cosmology in ghost-free [formula omitted] gravity

The improved version of ghost-free f(G) gravity introduced in Nojiri and Odintsov (2005) is proposed and investigated. It is demonstrated that improved ghost-free f(G) gravity may be consistently applied to describe the expanding universe (with horizon) as well as the static spacetime like black holes. Interestingly, such a theory looks like a close avatar of scalar-Einstein–Gauss–Bonnet gravity with the only difference that the scalar field is not a dynamical one so that many predictions of ghost-free f(G) gravity are very similar to that of sEGB gravity.We discuss the gravitational wave in the improved model with the condition that the propagating speed of the gravitational wave is identical to that of the propagation speed of light. A model that describes inflation in the early universe and could satisfy the observational constraints is also constructed. The solution of ghost-free f(G) gravity realising the given static spacetime with spherical symmetry is proposed. Some of such solutions realise explicitly the Reissner–Nordström black hole or the Hayward black hole, which is a regular black hole without curvature singularity, We also construct a black hole in our theory which contains the Arnowitt–Deser–Misner (ADM) mass, the horizon radius, and the radius of the photon sphere as independent parameters. The radius of the black hole shadow in this model as well as photon sphere radius are estimated. It is shown that there exists a parameter region which satisfies the constraints coming from Event Horizon Telescope observations. Furthermore, we construct model where the radius of the black hole shadow or photon orbit is smaller than the horizon radius supposed from the ADM mass.

Casimir wormholes inspired by electric charge in Einstein–Gauss–Bonnet gravity

This investigation assesses the feasibility of a traversable wormhole by examining the energy densities associated with charged Casimir phenomena. We focus on the influence of the electromagnetic field created by an electric charge as well as the negative energy density arising from the Casimir source. We have developed different shape functions by defining energy densities from this combination. This paper explores various configurations of Casimir energy densities, specifically those occurring between parallel plates, cylinders and spheres positioned at specified distances from each other. Furthermore, the impact of the generalized uncertainty principle correction is also examined. The behavior of wormhole conditions is evaluated based on the Gauss–Bonnet coupled parameter (μ) and electric charge (Q) through the electromagnetic energy density constraint. This is attributed to the fact that the electromagnetic field satisfies the characteristic ρ = −p r . Subsequently, we examine the active gravitational mass of the generated wormhole geometries and explore the behavior of μ and Q concerning active mass. The embedding representations for all formulated shape functions are examined. Investigations of the complexity factor of the charged Casimir wormhole have demonstrated that the values of the complexity factor consistently fall within a particular range in all scenarios. Finally, using the generalized Tolman–Oppenheimer–Volkoff equation, we examine the stability of the resulting charged Casimir wormhole solutions.

Charged AdS black holes with higher derivative corrections in the presence of string cloud

We have obtained charged asymptotically anti-de Sitter (AdS) black hole solutions in Einstein–Gauss–Bonnet gravity in the presence of string cloud. It turns out that there exist three black holes in certain range of parameters for small enough chemical potential. However, for large chemical potential, these black holes merge into a single one. The free energy of the black holes is computed from the on-shell Euclidean action by subtracting the contribution of an extremal black hole. We have studied the free energy and specific heat of the solutions, which shows that the medium-sized black hole is unstable. As an application, we have studied the quark–antiquark potential in the dual gauge theory. This study provides necessary ingredients for the study of the dual theories in the context of condensed matter systems.

Cosmic scenario with Einstein–Gauss–Bonnet gravity

By taking into account the Einstein–Gauss–Bonnet dilaton-coupled interaction in the background of the Robertson–Walker metric, we provide some bouncing solutions of the early universe from analytic solutions of the field equations for vanishing three space curvature. For a few potentials, the solutions involving the slow-roll-type approximation produce results that are very same to those of the early era’s bouncing solutions. Considering a different approach of slow-roll approximation, the universe goes through much faster initially than standard inflation, but at a later stage, the universe enters into standard exponential inflation.

Holographic transport in anisotropic plasmas

We study energy-momentum and charge transport in strongly interacting holographic quantum field theories in an anisotropic thermal state by contrasting three different holographic methods to compute transport coefficients: standard holographic calculation of retarded Green’s functions, a method based on the null-focusing equation near horizon and the novel method based on background variations. Employing these methods we compute anisotropic shear and bulk viscosities and conductivities with anisotropy induced externally, for example by an external magnetic field. We show that all three methods yield consistent results. The novel method allows us to read off the transport coefficients from the horizon data and express them in analytic form from which we derive universal relations among them. Furthermore we extend the method based on the null-focusing equation to Gauss-Bonnet theory to compute higher derivative corrections to the aforementioned transport coefficients. Published by the American Physical Society 2024