It has recently been argued that there may be a nontrivial four-dimensional limit of the higher-dimensional Gauss--Bonnet and Lovelock interactions and that this might provide a loophole allowing for new four-dimensional gravitational theories, possibly without a standard Lagrangian. We investigate this claim by studying tree-level graviton scattering amplitudes, allowing us to draw conclusions independently of the Lagrangian. By taking four-dimensional limits of higher-dimensional scattering amplitudes of the Gauss--Bonnet theory, we find four-dimensional amplitudes that are different from general relativity; however, these amplitudes are not new since they all come from certain scalar-tensor theories. The nontrivial limit that does not lead to infinite strong coupling around flat space leads to $(\partialϕ)^4$ theory. We argue that there cannot be any six-derivative purely gravitational four-point amplitudes in any dimension other than those coming from Lovelock theory by directly constructing the on-shell amplitudes. In particular, there can be no new such amplitudes in four dimensions beyond those of general relativity. We also present some new results on the spin-averaged cross section for graviton-graviton scattering in general relativity and Gauss--Bonnet theory in arbitrary dimensions.
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…
To ensure the existence of a well defined linearized gravitational wave equation, we show that the spacetimes in the so-called "Einstein-Gauss-Bonnet gravity in four dimension" have to be locally conformally flat.
We discuss a new extended gravity model in ordinary $D=4$ spacetime dimensions, where an additional term in the action involving Gauss-Bonnet topological density is included without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. Avoiding the Gauss-Bonnet density becoming a total derivative is achieved by employing the formalism of metric-independent non-Riemannian spacetime volume-forms. The non-Riemannian volume element triggers dynamically the Gauss-Bonnet scalar to become an arbitrary integration constant on-shell. We describe in some det…
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…
The topological classification of critical points of black holes in 4D Einstein-Gauss-Bonnet gravity coupled to Born-Infeld theory is investigated. Considered independently, Born-infeld corrections to the Einstein action alter the topological charge of critical points of the charged AdS black hole system, whereas the Gauss-Bonnet corrections do not. For the combined system though, the total topological charge of the Einstein-Gauss-Bonnet theory is unaltered in the presence of Born-Infeld coupling.
We propose a new model of $D=4$ Gauss-Bonnet gravity. To avoid the usual property of the integral over the standard $D=4$ Gauss-Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D=4 Gauss-Bonnet action term non-trivial without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss-Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cos…
We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol…
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black hole's background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increase…
We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and non-minimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the non-minimally coupling constant, the spacetime dimension, the cosmological constant and the Gauss-Bonnet coefficient in detail. We find that the non-minimal coupling may suppress the Hawking radiation, while the Gauss-Bonnet coupl…
In this paper we consider the holographic DC and Hall conductivity in Einstein-Maxwell-Dilaton in Gauss-Bonnet gravity with momentum dissipation. We analytically derived the DC conductivity and Hall conductivity from the black horizon data, and found that the conductivities are independent on the Gauss-Bonnet coupling. We also used the entropy function formalism to get the conductivities in terms of the charge of the black hole, even without knowing the explicit black hole solutions.
We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given in both the metric and the first order formalisms.
We investigate the shadows and photon spheres of the four-dimensional Gauss-Bonnet black hole with the static and infalling spherical accretions. We show that for both cases, the shadow and photon sphere are always present. The radii of the shadow and photon sphere are independent of the profiles of accretion for a fixed Gauss-Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion in this case. Because of the Doppler effect, the shadow of the infalling accretion is found to be darker than that of the static one. We also inves…
We study the greybody factor and power spectra of Hawking radiation for the minimally or nonminimally coupled scalar field with exact numerical method in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole spacetime. The effects of scalar coupling constant, angular momentum number of scalar, spacetime dimension, cosmological constant and Gauss-Bonnet coupling constant on the Hawking radiation are studied in detail. Specifically, the Gauss-Bonnet coupling constant always increases the greybody factor in the entire energy regime. Different from the case of Schwarzschild-de Sitter bl…
We obtain rotating black hole solutions to the novel 3D Gauss-Bonnet theory of gravity recently proposed. These solutions generalize the BTZ metric and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts, whose properties we also discuss. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss-Bonnet rotating black strings.
We revisit the Einstein-Gauss-Bonnet theory in view of the GW170817 event, which compels that the gravitational wave speed is equal to $c_T^2=1$ in natural units. We use an alternative approach compared to one previous work of ours, which enables us to express all the slow-roll indices and the observational indices as functions of the scalar field. Using our formalism we investigate if the Swampland criteria are satisfied for the Einstein-Gauss-Bonnet theory and as we demonstrate, the Swampland criteria are satisfied for quite general forms of the potential and the Gauss-Bonnet coupling functi…
Regularization of Gauss-Bonnet Gravity in Riemann-Cartan Geometry
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州高等研究院，UCAS）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University（湖南师范大学物理与量子效应及应用协同创新中心）
We consider spherically symmetric and static charged black holes in Einstein-Gauss-Bonnet-Maxwell gravities in general $D\ge 5$ dimensions and study their photon spheres and black hole shadows. We show that they all satisfy the sequence of inequalities recently proposed relating a black hole's horizon, photon sphere, shadow and its mass.
Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
在扩展相空间中研究了D维带电Gauss-Bonnet-AdS黑洞巨正则系综的热力学性质。我们发现，当五维球形带电Gauss-Bonnet-AdS黑洞的势固定在$0<Φ<\frac{\sqrt{3}π}{4}$范围内时，通常的小-大黑洞相变（与Van de Waals液-气系统类似）在五维球形带电Gauss-Bonnet-AdS黑洞中成立.对于其他高维拓扑带电的Gauss-Bonnet-AdS黑洞，则不存在这种相变。在Reissner-Nordstrom-AdS黑洞的极限情形下，当Gauss-Bonnet参数为零时，巨正则系综不存在临界行为.这个结果与时空维度和拓扑无关。我们还研究了五维球形带电Gauss-Bonnet-AdS黑洞临界点附近物理量的行为。
Applying the large $D$ approach to the Einstein-Gauss-Bonnet theory, we construct equally rotating black hole solutions in odd dimensions. This provides the first example of the analytic solutions which describes not-slowly rotating black holes. For the next-leading order solutions in the $1/D$ expansion, we discuss the physical aspects such as thermodynamics and the phase diagram.
In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.
Recently, Kumar and Ghosh have derived Kerr-like rotating black hole solutions in the framework of four-dimensional Einstein-Gauss-Bonnet theory of gravity and investigated the black hole shadow. Using the steady-state Novikov-Thorne model, we study thin accretion disk processes for such rotating black holes including the energy flux, temperature distribution, emission spectrum, energy conversion efficiency as well as the radius of the innermost stable circular orbit. We also study the effects of the Gauss-Bonnet coupling parameter $α$ on these quantities. The results are compared to slowly ro…
The innermost stable circular orbits (ISCOs) around rapidly rotating neutron stars are studied in dilatonic Einstein-Gauss-Bonnet theory. Universal relations for properly scaled ISCO properties are extended from General Relativity to dilatonic Einstein-Gauss-Bonnet theory and additional relations are obtained.
