Gauss-Bonnet Term Research Articles

Optical Features of AdS Black Holes in the Novel 4D Einstein-Gauss-Bonnet Gravity Coupled to Nonlinear Electrodynamics

An alternative theory of gravity that has attracted much attention recently is the novel four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. The theory is rescaled by the Gauss-Bonnet (GB) coupling constant α→α/(D−4) in D dimensions and redefined as four-dimensional gravity in the limit D→4. Thus, in this manner, the GB term yields a non-trivial contribution to the gravitational dynamics. In fact, regularized black hole solutions and applications in the novel 4D EGB gravity have also been extensively explored. In this work, motivated by recent astrophysical observations, we present an in-depth study of the optical features of AdS black holes in the novel 4D EGB gravity coupled to exponential nonlinear electrodynamics (NED), such as the shadow geometrical shape, the energy emission rate, the deflection angle and quasinormal modes. Taking into account these dynamic quantities, we investigate the effects on the black hole solution by varying the parameters of the models. More specifically, we show that the variation of the GB and NED parameters, and of the cosmological constant, imprints specific signatures on the optical features of AdS black holes in the novel 4D EGB gravity coupled to nonlinear electrodynamics, thus leading to the possibility of directly testing these black hole models by using astrophysical observations.

On stable exponential cosmological solutions with two factor spaces in (1+ m + 2)-dimensional Einstein-Gauss-Bonnet model with Λ-term.

A [Formula: see text]-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term [Formula: see text] is considered. Exact solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters [Formula: see text] and [Formula: see text], corresponding to factor spaces of dimensions [Formula: see text] and [Formula: see text], respectively, are found. Under certain restrictions on [Formula: see text], the stability of the solutions in a class of cosmological solutions with diagonal metrics is proved. A subclass of solutions with small enough variation of the effective gravitational constant [Formula: see text] is considered and the stability of all solutions from this subclass is shown. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

Anisotropic Compact Stars in D → 4 Limit of Gauss–Bonnet Gravity

In the frame of Gauss–Bonnet gravity and in the limit of D→4, based on the fact that spherically symmetric solution derived using any of regularization schemes will be the same form as the original theory, we derive a new interior spherically symmetric solution assuming specific forms of the metric potentials that have two constants. Using the junction condition we determine these two constants. By using the data of the star EXO 1785-248, whose mass is M=1.3±0.2M⊙ and radius l=8.849±0.4 km, we calculate the numerical values of these constants, in terms of the dimensionful coupling parameter of the Gauss–Bonnet term, and eventually, we get real values for these constants. In this regard, we show that the components of the energy–momentum tensor have a finite value at the center of the star as well as a smaller value to the surface of the star. Moreover, we show that the equations of the state behave in a non-linear way due to the impact of the Gauss–Bonnet term. Using the Tolman–Oppenheimer–Volkoff equation, the adiabatic index, and stability in the static state we show that the model under consideration is always stable. Finally, the solution of this study is matched with observational data of other pulsars showing satisfactory results.

Late time cosmology in -gravity with interacting fluids

Cosmological models are obtained in a f(R) modified gravity with a coupled Gauss–Bonnet (GB) terms in the gravitational action. The dynamical role of the GB terms is explored with a coupled dilaton field in two different cases (I) where γ, λ and δ are arbitrary constants and (II) f(R) = R and estimate the constraints on the model parameters. In the first case we choose GB terms coupled with a free scalar field in the presence of interacting fluid and in the second case GB terms coupled with scalar field in a self interacting potential to compare the observed Universe. The evolutionary scenario of the Universe is obtained adopting a numerical technique as the field equations are highly non-linear. Defining a new density parameter Ω H , a ratio of the dark energy (DE) density to the present energy density of the non-relativistic matter, we look for a late accelerating Universe. The state finder parameters Ω H , deceleration parameter (q), jerk parameter (j) are plotted. It is noted that a non-singular Universe with oscillating cosmological parameters for a given strength of interactions is admitted in model-I. The gravitational coupling constant λ is playing an important role. The Lagrangian density of f(R) is found to dominate over the GB terms when oscillating phase of DE arises. In model-II, we do not find oscillation of the cosmological parameters as the Universe evolves. In the presence of interaction the energy from radiation sector of matter cannot flow to the other two sectors of fluid. The range of values of the strengths of interaction of the fluids are estimated for a stable Universe assuming the primordial gravitational wave speed equal to unity.

Rotating charged black hole in 4D Einstein–Gauss–Bonnet gravity: Photon motion and its shadow

We construct a charged rotating black hole in 4D Einstein–Gauss–Bonnet (EGB) gravity starting from charged black hole in 4D EGB gravity using complex coordinate transformations suggested by Newman–Janis. Further, we have studied the null geodesics to investigate the shape of the shadow cast by a rotating charged black hole in 4D EGB gravity. Also we have discussed their horizon properties and shadow cast. The phenomenon of black hole shadows alongwith the horizon structure and energy emission has been analyzed to see the influence of Gauss–Bonnet term and black hole charge on horizon, shadow, effective potential and energy emission rate which are compared to their non rotating counterpart. It has been seen that the Gauss–Bonnet parameter have an influence on the shape and size of the shadow as well as on the effective potential, horizon and energy emission rate.

Complexity of dynamical cylindrical system in f(G, T) gravity

The purpose of this paper is to formulate a complexity factor for a non-static cylindrical structure in the background of [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] represent the Gauss–Bonnet term and trace of the energy–momentum tensor, respectively. Different physical factors such as inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms are considered as candidates of complexity. In order to determine a complexity factor encompassing the essential aspects of the system, we apply the technique of orthogonal splitting to the Riemann tensor. We also study evolution of the cylinder through two modes: homologous and homogeneous. Further, we utilize the complexity-free and homologous conditions to examine the dissipative and non-dissipative self-gravitating system. Finally, the factors responsible for inducing complexity during the evolution system are inspected. We deduce that the modified terms in [Formula: see text] gravity make the system more complex.

Charged polytropic compact stars in [formula omitted] Einstein–Gauss–Bonnet gravity

We have investigated the possibility of existing a class of compact charged spheres made of a charged perfect fluid in the context of recently proposed 4D Einstein–Gauss–Bonnet (EGB) gravity theory. The main mechanism is to rescale the Gauss–Bonnet (GB) coupling constant α→α/(D−4) in D dimensions and redefining the 4D gravity in the limit D→4. In this way, the GB term yields a non-trivial contribution to the gravitational dynamics in 4D. Our analysis is based on the assumption of a polytropic equation of state (EoS) and the charge density is taken to be proportional to the energy density. More specifically, we have derived the hydrostatic equilibrium equations in 4D EGB, and we have solved them numerically to obtain mass–radius relations for charged compact stars. Eventually we have found the mass–radius relation depending on the values of the GB coupling constant α and the charge fraction ρch(r). In addition, we have studied the mass vs central mass density (M−εc) relation, which identifies the boundary separating the stable configuration region from the unstable one. We have also obtained a relation between the electric charge inside the stellar region and the maximum mass of compact star in this gravity theory. Finally, we conclude that in such a scenario charged stars may exist in Nature, and that such a deviation may be observable in future astrophysical probes.

A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).

Quadratic curvature corrections to stringy effective actions and the absence of de Sitter vacua

We investigate the combined effect of fluxes and higher-order curvature corrections, in the form of the Gauss-Bonnet term, on the existence of de Sitter vacua in a heterotic string inspired framework, compactified on spheres and tori. We first gain some intuition on the effects of these corrections by studying a perturbative expansion in the small Gauss-Bonnet coupling. Then, for choices of potential closer to the string theory predictions, we show that the inclusion of quadratic curvature corrections actually reduces the parametric likelihood of de Sitter solutions.

Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime

We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector. We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme. We also obtain a Schwarzschild-like bumblebee black hole solution in D-dimensional spacetime. We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential. That is, its gravitational potential has a minimum value (negative) in the black hole interior and has a positive value 1+ℓ at short distance r→0. If the constant ℓ is large enough, then this kind of black hole is practically free from the singularity problem. The thermodynamics and phase transition are also studied. In a cosmological context, it is interesting that the Gauss-Bonnet term has no effect on the conservation of energy equation. A late-time expansion of de Sitter universe can be replicated in an empty space. The Gauss-Bonnet term and the bumblebee field can both actually act as a form of dark energy.

Inflation with Gauss-Bonnet Term and Novelcouplings

Inflation with Gauss-Bonnet Term and Novelcouplings

A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases

A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

Exploring the self-tuning of the cosmological constant from Planck mass variation

Recently, the variation of the Planck mass in the general relativistic Einstein–Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing standard model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the local self-tuning action by a coupled Gauss–Bonnet term and a companion four-form field strength, graviton loops can be prevented from incapacitating the degravitation of the standard model vacuum energy. For certain cases, we furthermore find that this extension can be recast as a Horndeski scalar–tensor theory and be embedded in the conventional local self-tuning formalism. We then explore the possibility of a unification of inflation with self-tuning. The resulting equations can alternatively be used to motivate a multiverse interpretation. In this context, we revisit the coincidence problem and provide an estimation for the probability of the emergence of intelligent life in our Universe as a function of cosmic age, inferred from star and terrestrial planet formation processes. We conclude that we live at a very typical epoch, where we should expect the energy densities of the cosmological constant and matter to be of comparable size. For a dimensionless quantity to compare the emergence of life throughout the cosmic history of different universes in an anthropic analysis of the multiverse, we choose the order of magnitude difference of the evolving horizon size of a Universe to the size of its proton as the basic building block of atoms, molecules, and eventually life. For our Universe we find this number to form peak at approximately 42. We leave the question of whether the same number is frequently assumed for the emergence of life across other universes or singles out a special case to future exploration.

Null shells and double layers in quadratic gravity

For a singular hypersurface of arbitrary type in quadratic gravity motion equations were obtained using only the least action principle. It turned out that the coefficients in the motion equations are zeroed with a combination corresponding to the Gauss-Bonnet term. Therefore it does not create neither double layers nor thin shells. It has been demonstrated that there is no “external pressure” for any type of null singular hypersurface. It turned out that null spherically symmetric singular hupersurfaces in quadratic gravity cannot be a double layer, and only thin shells are possible. The system of motion equations in this case is reduced to one which is expressed through the invariants of spherical geometry along with the Lichnerowicz conditions. Spherically symmetric null thin shells were investigated for spherically symmetric solutions of conformal gravity as applications, in particular, for various vacua and Vaidya-type solutions.

Primordial black holes from Gauss-Bonnet-corrected single field inflation

Primordial blackholes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial blackholes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial blackholes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism for the primordial blackhole formation. We consider a model in which a scalar field is coupled to the Gauss-Bonnet term and show that primordial blackholes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial blackholes but it also sources gravitational waves at the second order. We calculate the present density parameter of the gravitational waves and discuss the detectability of the signals by comparing them with sensitivity bounds of future gravitational wave experiments.

Wormhole solutions and energy conditions in f(R,G) gravity

In this manuscript, the traversable wormhole solutions have been explored in modified gravity by taking into consideration the model , where R is the Ricci curvature scalar and G is the Gauss–Bonnet term. An acceptable form of the redshift function has been incorporated which is a non-constant in nature along with the implementation of those already defined in literature, the two shape functions namely and . It is shown by studying the energy condition and through the graphical analysis that the null energy bounds for the effective energy-momentum tensor are generally violated for the presence of the ordinary matter in modified gravity. Energy conditions associated with the matter content threading the wormhole geometries are evaluated and in general are found to favor the null energy conditions in the vicinity of the wormhole throat, the existence of the non-exotic wormhole geometries threaded by the matter has been confirmed under this gravity.

Inflation with Gauss–Bonnet and Chern–Simons higher-curvature-corrections in the view of GW170817

Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einstein’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. As a result, formed a system of differential equations with respect to Hubble’s parameter and the inflaton field which was very complicated and cannot be solved analytically, even in the minimal coupling case. Based on the observations from GW170817 event, which have shown that the speed of the primordial gravitational wave is equal to the speed of light, \(c_{\mathcal {T}}^2=1\) in natural units, our equations of motion where simplified after applying the constraint \(c_{\mathcal {T}}^2=1\), the slow-roll approximations and neglecting the string corrections. We described the dynamics of inflationary phenomenology and proved that theories with Gauss–Bonnet term can be compatible with recent observations. Also, the Chern–Simons term leads to asymmetric generation and evolution of the two circular polarization states of gravitational wave. Finally, viable inflationary models are presented, consistent with the observational constraints. The possibility of a blue tilted tensor spectral index is briefly investigated.

Charged black hole in 4D Einstein-Gauss-Bonnet gravity: particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy

We study the motion of charged and spinning particles and photons in the 4D charged Einstein-Gauss-Bonnet (EGB) black hole vicinity. We determine the radius of the innermost stable circular orbit (ISCO) for test particles. We show that the combined effect of the Gauss-Bonnet (GB) coupling parameter and black hole charge decreases the ISCO and the radius of the photon sphere. Further, we study the gravitational deflection angle and show that the impact of GB term and black hole charge on it is quite noticeable. We also consider the effect of plasma and find the analytical form of the deflection angle in the case of a uniform and non-uniform plasma. Interestingly we find that the deflection angle becomes larger when uniform plasma is considered in comparison to the case of non-uniform plasma. We also study the center of mass energy (E C.M.) obtained by collision process for non-spinning particles and show that the impact of GB parameter and black hole charge leads to high energy collision. In addition, we also study the E C.M. for the case of spinning particles and show that if the two spinning particles collide near the horizon of 4D charged EGB BH, the E C.M. becomes infinitely high which is in disparity with the non-spinning particles counterpart where E C.M. never grows infinitely. To achieve this, an important role is played by the spinning particle known as the near-critical particle (i.e. a particle with fine-tuned parameters). In order to achieve the unbounded E C.M. from the collision of two spinning particles, the energy per unit mass must be less than unity for a near-critical particle, which means such a particle starts from some intermediate position r > rh and not from infinity.

Charged spherical solution in [formula omitted] gravity via embedding

The present article discusses a charged spherical solution in modified f(G,T) gravity under the embedding class I condition, where f(G,T)=G2+χT, where G is a Gauss–Bonnet term and T denotes a trace of energy momentum tensor, while χ is called coupling constant. The Exact solution of the Einstein–Maxwell’s field equations in f(G,T) gravity is obtained by taking a particular ansatz for radial component of the line element. The validity of the charged spherical solution has been tested via different physical analysis. The physical analysis shows that the present solution is well behaved. Moreover, we plotted the graphs for a particular star Vela X-1 for different χ, which show the trends of the thermodynamical observables like pressure, density, electric charge, energy conditions as well as impact of χ parameter on the above thermodynamical observables. On the other hand, we predicted the radii for 12 stars with different χ. The mass–radius ratio and surface red-shift are also calculated. Also, we have discussed the stability and equilibrium condition of the solution. Overall, the above analysis shows that obtained solution describes a physically viable and stable compact star. The prediction of radii from GW 170817 is also in agreement with our M−R curve.

Rotating scalarized black holes in scalar couplings to two topological terms

The tachyonic instability of the Kerr black holes is analyzed in the Einstein-scalar theory with the quadratic scalar couplings to two topological terms which are parity-even Gauss-Bonnet and parity-odd Chern-Simons terms. For positive coupling α, we use the (2+1)-dimensional hyperboloidal foliation method to derive the threshold curve which is the boundary between stable and unstable Kerr black holes by considering a spherically symmetric scalar-mode perturbation. In case of negative coupling, a newly bound of a≥0.26 with a the rotation parameter is found for unstable Kerr black holes and its threshold curve is derived.