The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2+1 model universes. For the relevant 3+1 case, we employ a method based on the Gauss-Bonnet-Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3+1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.
In this paper we show positive mass theorems and Penrose type inequalities for the Gauss-Bonnet-Chern mass, which was introduced recently in \cite{GWW}, for asymptotically flat CF manifolds and its rigidity.
We give an explicit formula for the Gauss-Bonnet-Chern mass of an asymptotically flat graphical manifold of arbitrary codimension and use it to prove the positive mass theorem and the Penrose inequality for graphs with flat normal bundle.
We study the problem of boundary terms and boundary conditions for Chern-Simons gravity in five dimensions. We show that under reasonable boundary conditions one finds an effective field theory at the four-dimensional boundary described by dilaton gravity with a Gauss-Bonnet term. The coupling of matter is also discussed.
In this paper we introduce a family of center of masses that complement the definition of the family of Gauss-Bonnet-Chern masses by Ge-Wang-Wu and Li-Nguyen. In order to prove the existence and the well-definedness of the center of mass, we use the formalism of double forms of Kulkarni and Labbi. This allows for transparent conceptual proofs, which apply to all known cases of asymptotic invariants of asymptotically flat manifolds.
Following the previous work 1103.3773, we give a more general and systematic discussion on the Chern-Simons effect in the 5-dimensional Maxwell-Gauss-Bonnet gravity. After constructing the first order perturbative black brane solution, we extract the stress tensor and charge current of dual fluid. From these results, we find out the dependence of some transport coefficients on the Gauss-Bonnet coupling $α$ and Chern-Simons coupling $κ_{cs}$. We also show that the new anomalous term can provide an additional contribution to the anomalous chiral magnetic conductivity.
We carry out the stability analysis of the Schwarzschild black hole in Gauss-Bonnet and Chern-Simons-scalar theory. Here, we introduce two quadratic scalar couplings ($ϕ_1^2,ϕ_2^2$) to Gauss-Bonnet and Chern-Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar $ϕ_1$ is the Klein-Gordon equation with an effective mass, while the perturbation equation for $ϕ_2$ is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against …
We study slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections. We obtain general formulas for the observables: spectral indices, tensor-to-scalar ratio and circular polarization of gravitational waves. The Gauss-Bonnet term violates the consistency relation r = -8n_T. Particularly, blue spectrum n_T > 0 and scale invariant spectrum |8n_T|/r << 1 of tensor modes are possible. These cases require the Gauss-Bonnet coupling function of ξ_{,ϕ} \sim 10^8/M_{Pl}. We use examples to show new-inflation-type potential with 10M_{Pl} symmetry breaking scale and potential with flat region…
The gravitational Chern-Simons term coupled to an evolving axion is known to generate lepton number through the gravitational anomaly. We examine this leptogenesis scenario in the presence of the Gauss-Bonnet term over and above the gravitational Chern-Simons term. We find that the lepton production can be exponentially enhanced. The Gauss-Bonnet term creates CP-violating instability of gravitational waves that may appear transiently after inflation, and during the period of instability elliptically polarized gravitational waves are exponentially amplified at sub-horizon scales. This instabili…
Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a result two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated type Klein) surfaces are derived.
The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k=1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metric…
We discuss the recently suggested Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity. We have tested some general forms of the scale factor $a(t)$, and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration-acceleration transition, and it has appeared in othe…
Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einsteins's gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss-Bonnet and Chern-Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. A…
In the present work we study (i) charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) black hole in EGB gravity with Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.
In this paper, we will generalize the Gauss-Bonnet gravity to an energy dependent Gauss-Bonnet theory of gravity, which we shall call as the Gauss-Bonnet gravity's rainbow. We will also couple this theory to a Maxwell's theory. We will analyze black hole solutions in this energy dependent Gauss-Bonnet gravity's rainbow. We will calculate the modifications to the thermodynamics of black holes in the Gauss-Bonnet's gravity's rainbow. We will demonstrate that even though the thermodynamics of the black holes get modified in the Gauss-Bonnet gravity's rainbow, the first law of thermodynamics still…
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.
This paper deals with five-dimensional black hole solutions in (a) Einstein-Yang-Mills-Gauss-Bonnet theory and (b)Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant for spherically symmetric space time. The geometry of the black hole thermodynamics has been studied for both the black holes.
In this paper we investigate the strong gravitational lensing with Gauss-Bonnet gravity. By considering the logarithmic term for deflection angle, we obtain the deflection angle $\hatα$ and corresponding parameters $\bar{a}$ and $\bar{b}$. Finally, by using the relations between the observables and lensing parameters, we estimate the observables such as, $θ_{\infty}$, $s$ and $r_m$, for the relativistic images in the Gauss-Bonnet background.
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…
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 write down an anisotropic solution for a flat 5+1 dimensional Universe in Gauss-Bonnet gravity. In the model under investigation this solution replaces the generalized Kasner solution near a cosmological singularity.
We consider the Gauss-Bonnet corrected Bardeen black hole solution in 4-D AdS space-time. The solution is obtained by the limiting procedure adopted by Glavan and Lin in 4-D Einstein-Gauss-Bonnet gravity. The general form of first law of black hole thermodynamics is utilized to calculate various thermodynamics variables. The solution exhibit P-v criticality and belong to the universality class of van-der Waals fluid. The effect of Gauss-Bonnet coupling is investigated on critical parameters and inversion temperature.
The time delay between two relativistic images in the strong gravitational lensing governed by Gauss-Bonnet gravity is studied. We derive and calculate the expression of time delay due to the Gauss-Bonnet coupling. It is shown that the time delay for two images with larger space each other is longer. We also find that the ratio of Gauss-Bonnet coefficient and the mass of gravitational source changes in the region like $\fracα{M}\in[0,2)$. The time delay is divergent with $\fracα{M}\longrightarrow 2$.
We study the massless scalar, Dirac and electro-magnetic fields propagating on a 4D-brane, which is embedded in higher dimensional Gauss-Bonnet space-time. We calculate, in time-domain, the fundamental quasi-normal modes of a spherically symmetric black hole for such fields. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at asymptotically late time.
The influence of non-minimal coupling of a scalar field and the Gauss-Bonnet term on the inflationary stage of evolution of the universe is investigated in this paper. The main cosmological effects of such a coupling were considered. The deviations between Einstein-Gauss-Bonnet inflation and standard one based on Einstein gravity were determined. The corrections of a weak GB coupling preserving the type of the scalar field potential to standard inflationary models is considered as well.
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.
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 o…
We have investigated tidal forces and geodesic deviation motion in the 4D-Einstein-Gauss-Bonnet spacetime. Our results show that tidal force and geodesic deviation motion depend sharply on the sign of Gauss-Bonnet coupling constant. Comparing with Schwarzschild spacetime, the strength of tidal force becomes stronger for the negative Gauss-Bonnet coupling constant, but is weaker for the positive one. Moreover, tidal force behaves like those in the Schwarzschild spacetime as the coupling constant is negative, and like those in Reissner-Nordström black hole as the constant is positive. We also pr…
We consider black hole in Einstein-Gauss-Bonnet(EGB) gravity in a dynamical setup and also the stationary black hole in recently discovered\cite{Glavan} $4$-dimensional novel Einstein-Gauss-Bonnet gravity. For dynamical EGB black hole in completely local settings we calculate the temperature associated with the horizon. For the stationary black hole in $4$-dimensional novel EGB theory we explore the thermodynamic properties including calculation of temperature and entropy.
By adopting the 5D version of the Wu-Yang Ansatz we present in closed form a black hole solution in the Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) theory. In the EYM limit, we recover the 5D black hole solution already known.
We investigate the absorption cross section of planar scalar massless waves impinging on spherically symmetric black holes which are solutions of the novel 4D Einstein-Gauss-Bonnet theory of gravity. Besides the mass of the black hole, the solution depends also on the Gauss-Bonnet constant coupling. Using the partial waves approach, we show that the absorption cross section depends on the Gauss-Bonnet coupling constant. Our numerical results present excellent agreement with the low- and high- frequency approximations, including the so-called sinc approximation.
We study the phase space of the spherically symmetric solutions of Einstein Gauss-Bonnet system nonminimally coupled to a scalar field and show that in four dimensions the only regular black hole solutions are asymptotically flat
In this paper, we first use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.
We study the cosmological model based on Einstein-Gauss-Bonnet gravity with non-minimal coupling of a scalar field to a Gauss-Bonnet term in 4D Friedmann universe. We show how constructing the exact solutions by the method based on a confrontation of the Hubble parameter in the model under consideration with that in a standard scalar field inflationary cosmology.
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss-Bonnet action with a cosmological constant. We show that all the physical solutions have anti-de Sitter asymptotic behavior.
We study the phase space of the spherically symmetric solutions of Einstein-Maxwell-Gauss-Bonnet system nonminimally coupled to a scalar field and prove the existence of solutions with unusual asymptotics in addition to asymptotically flat ones. We also find new dyonic solutions of dilatonic Einstein-Maxwell theory.
A Vaidya-based model of a radiating black-hole is studied in a 5-dimensional Einstein gravity with Gauss-Bonnet contribution of quadratic curvature terms. The structure and locations of the apparent and event horizons of the radiating black hole are determined.
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 consider the five-dimensional Einstein-Gauss-Bonnet gravity, which can be obtained by means of an apropriate choice of coeficients in the five-dimensional Lanczos-Lovelock gravity theory. The Einstein-Gauss-Bonnet field equations for the Friedmann-Lemaître-Robertson-Walker metric are found as well as some of their solutions. A four-dimensional gravity action is obtained from the Gauss-Bonnet gravity using the Randall-Sundrum compactification procedure and then it is studied the implications of the compactification procedure in the cosmological solutions. The same procedure is used to obtain…
The influence of the Maxwell field on a static, asymptotically flat and spherically-symmetric Gauss-Bonnet black hole is considered. Numerical computations suggest that if the charge increases beyond a critical value, the inner determinant singularity is replaced by an inner singular horizon.
We study the asymptotic behavior of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein- Gauss-Bonnet action. We show that in general the scalar field that parametrizes the size of the internal space is not trivial, but nevertheless the solutions depend on a single parameter. In analogy with other models containing Gauss-Bonnet terms, naked singularities are avoided if a minimal radius for the horizon is assumed.
The purpose of this Comment is to point out that there are conceptual and mathematical flaws in the analysis in "Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem, Phys. Rev. D 98, 044033 (2018) by Ali Övgün".
The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity…
We have studied the polarized image of an equatorial emitting ring around a 4D Gauss-Bonnet black hole. Our results show that the effects of Gauss-Bonnet parameter on the polarized image depend on the magnetic field configuration, the observation inclination angle, and the fluid velocity. As the magnetic field lies in the equatorial plane, the observed polarization intensity increases monotonously with Gauss-Bonnet parameter in the low inclination angle case, and its monotonicity disappears in the case with high inclination angle. However, as the magnetic field is vertical to the equatorial pl…
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 $D\rightarrow 4$.
This paper gives a new, simple and concise derivation of brane actions and brane dynamics in general relativity and in Einstein-Gauss-Bonnet gravity. We present a unified treatment, applicable to timelike surface layers and spacelike transition layers, and including consideration of the more difficult lightlike case.
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss- Bonnet action. We show the existence of solutions with nonflat asymptotic behavior.
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…
A self-interacting SU(2)-doublet of complex scalar fields, minimally coupled to Einstein-Gauss-Bonnet gravity is considered in five space-time dimensions. The classical equations admit two families of solitons corresponding to spinning and non-spinning bosons stars. The generic solutions are constructed numerically and agree with exact results that are available in special limits of the parameters. The pattern of the boson stars is shown to be qualitatively affected by the Gauss-Bonnet coupling constant.
As an interesting application of the Einstein-Gauss-Bonnet theory and our work on the Gauss-Bonnet-Chern mass (Ge, Wang, Wu), we obtain a positive mass theorem for asymptotically flat graphs in $\R^{n+1}$ under a condition that $R+αL_2$ is non-negative, where $R$ is the scalar curvature, $α\in\R$ a constant and $L_2$ the second Gauss-Bonnet curvature. A Penrose type inequality is also obtained in the case $α>0$.
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.
The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-B…
