Recently Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] formulated a novel Einstein-Gauss-Bonnet gravity in which the Gauss-Bonnet coupling has been rescaled as $α/(D-4)$ and the $4D$ theory is defined as the limit $D \rightarrow 4$, which preserves the number degrees of freedom thereby free from the Ostrogradsky instability. We present exact spherically symmetric nonstatic null dust solutions in the novel 4D Einstein-Gauss-Bonnet gravity that bypasses the Lovelock theorem. Our solution represents radiating black holes and regains, in the limit $α\rightarrow 0$, the famous Vaidya black hole of general relativity (GR). We discuss the horizon structure of black hole solutions to find that the three horizon-like loci that characterizes its structure, viz. $AH$, $EH$ and $ TLS $ have the relationship $r_{EH} < r_{AH} = r_{TLS}$. The charged radiating black holes in the theory, generalizing Bonnor-Vaidya black holes, are also considered. In particular our results, in the limit $α\rightarrow 0$, reduced exactly to \emph{vis-$\grave{a}$-vis} 4D black holes of GR.
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.
This paper deals with the dynamics of a shearfree charged radiating collapse in modified Gauss-Bonnet gravity. The field equations for shearfree spherical interior geometry of a charged dissipative star are formulated. To study the dynamical behavior of collapsing matter, we derive the dynamical as well as transport equations. We conclude that the gravitational force in modified Gauss-Bonnet gravity is much stronger as compared to general relativity which implies the increase in the rate of collapse. Finally, we study the effect of charge on the dynamics of collapse.
In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in $n$-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as, the Gauss-Bonnet versions of the Bonnor-Vaidya(de Sitter/anti-de Sitter) solution, a global monopole and the Husain black holes. We also present a more …
The main purpose of this paper is to investigates structure scalars in the context of $f(\mathcal{G}, T)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet invariant and $T$ is the trace of stress energy tensor. For this aim, we have considered the spherically symmetric spacetime and dissipative anisotropic fluid coupled with radiation and heat ejecting shearing matter distributions. We have found these scalar variables by orthogonally decomposing the Riemann curvature tensor in $f(\mathcal{G}, T)$ gravity. Moreover, the evolution equations of shear and expansion are also developed with the hel…
We derive nonstatic spherically symmetric solutions of a null fluid, in five dimension (5D), to Einstein-Yang-Mills (EYM) equations with the coupling of Gauss-Bonnet (GB) combination of quadratic curvature terms, namely, 5D-EYMGB radiating black hole solution. It is shown that, in the limit, we can recover known radiating black hole solutions. The spherically symmetric known 5D static black hole solutions are also retrieved. The effect of the GB term and Yang-Mills (YM) gauge charge on the structure and location of horizons, of the 5D radiating black hole, is also discussed.
We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the ``dark radiation'' in the Gauss-Bonnet braneworld.
We present exact spherically symmetric null dust solutions in the third order Lovelock gravity with a string cloud background in arbitrary $N$ dimensions,. This represents radiating black holes and generalizes the well known Vaidya solution to Lovelock gravity with a string cloud in the background. We also discuss the energy conditions and horizon structures, and explicitly bring out the effect of the string clouds on the horizon structure of black hole solutions for the higher dimensional general relativity and Einstein-Gauss-Bonnet theories. It turns out that the presence of the coupling con…
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…
In recent times there is a surge of interest in constructing Einstein-Gauss-Bonnet (EGB) gravity, in the limit $D \to 4 $, of the $D$-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed $D \to 4 $ regularized EGB gravities coincide, and incidentally some other theories also admit the same solution. We prove a theorem that characterizes a large family of nonstatic or radiating spherically symmetric solutions to the $4D$ EGB gravity, representing, in general, spherically symmetric Type II fluid. An extension of the theorem, given without pro…
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.
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.
In the framework of an arbitrary $D$-dimensional metric theory, perturbations are considered on arbitrary backgrounds that are however solutions of the theory. Conserved currents for perturbations are presented following two known prescriptions: canonical Nœther theorem and Belinfante symmetrization rule. Using generalized formulae, currents in the Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds (not only vacuum) are constructed in an explicit covariant form. Special attention is paid to the energy-momentum tensors for perturbations whic…
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 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.
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…
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.
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.
We consider a Lemaitre - Tolman - Bondi type space-time in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms, and present exact solution in closed form. It turns out that the presence of the coupling constant of the Gauss-Bonnet terms alpha > 0 completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional Gauss-Bonnet extended Einstein equations leads to formation of a massive, but weak, timelike singularity which is forbidden in general relativity…
In this paper, we have investigated the dynamics of magnetized particles around 4-D Einstein-Gauss-Bonnet black hole immersed in an external asymptotically uniform magnetic field. We have shown that the magnetic interaction parameter responsible for circular orbits decreases for negative values of the Gauss-Bonnet parameter $α$ and the range where magnetized particle's stable circular orbits are allowed increases for the positive values of the parameter $α$. The study of the collisions of magnetized, charged and neutral particles has shown that the center-of-mass energy of the particles increa…
We investigate the dynamics of a d-dimensional domain wall (DW) in a d+1-dimensional Einstein-Gauss-Bonnet (EGB) bulk. Exact effective potential induced by the Gauss-Bonnet (GB) term on the wall is derived. In the absence of the GB term we recover the familiar gravitational and anti-harmonic oscillator potentials. Inclusion of the GB correction gives rise to a minimum radius of bounce for the Friedmann-Robertson-Walker (FRW) universe expanding with a negative pressure on the DW.
We explore static spherically symmetric stars in the Gauss-Bonnet gravity without cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the sta…
We study a solution of the Einstein-Gauus-Bonnet theory in 5 dimensions coupled to a Maxwell field, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.
We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configura…
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 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 $D\rightarrow 4$.
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…
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.
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.
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.
