Gauss-Bonnet Term Research Articles

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.

Fractional Einstein–Gauss–Bonnet Scalar Field Cosmology

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and α0=t0H0 and the fractional derivative order μ. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and α0, indicating that the solution is consistent with an accelerated expansion at late times with the values α0=1.38±0.05, m=1.44±0.05, and μ=1.48±0.17 (consistent with Ωm,0=0.311±0.016 and h=0.712±0.007), resulting in an age of the Universe t0=19.0±0.7 [Gyr] at 1σ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than ΛCDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.

Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity

Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein-Hilbert gravity. Projective geometry was used long ago by Thomas to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a “Rosetta Stone” between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant. Published by the American Physical Society 2024

Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity

Within the framework of Einstein-Gauss-Bonnet theory in five-dimensional spacetime (5D EGB), we derive the hydrostatic equilibrium equations and solve them numerically to obtain neutron stars for both isotropic and anisotropic distribution of matter. The mass-radius relations are obtained for SLy equation of state, which describes both the solid crust and the liquid core of neutron stars, and for a wide range of the Gauss-Bonnet coupling parameter α. More specifically, we find that the contribution of the Gauss-Bonnet term leads to substantial deviations from Einstein gravity. We also discuss that after a certain value of α, the theory admits higher maximum masses compared with general relativity, however, the causality condition is violated in the high-mass region. Finally, our results are compared with the recent observations data on mass-radius diagram.

Constraining [formula omitted] gravity by dynamical system analysis

In this paper, we have studied the different phases of the evolution of the Universe through the dynamical system analysis. Here we explored the f(T,B,TG,BG) gravity, where T, B, TG, and BG respectively represent torsion, boundary term, teleparallel Gauss–Bonnet term, and Gauss–Bonnet boundary term. The transformation f(T,B,TG,BG)=−T+F(T,B,TG,BG) has been incorporated to get the deviation from the Teleparallel Equivalent of General Relativity. Two well motivated cosmological models (i) F(T,B,TG,BG)=f0TmBnTGk and (ii) F(T,B,TG,BG)=b0B+g0TGk have been studied. The critical points representing different phases of evolution have been studied in details. Further with the help of the eigenvalues and phase space diagrams, the stability and attractor nature of the accelerating solutions have been explored. The evolution plots have been analysed for the corresponding cosmology. The compatibility of the evolution plots has been checked with standard density parameters at present time.

Theory of Classical Electrodynamics with Topologically Quantized Singularities as Electric Charges

AbstractA theory of classical electrodynamics, where the only admissible electric charges are topological singularities in the electromagnetic field, is formulated. Charge quantization is accounted by the Chern theorem, such that Dirac magnetic monopoles are not needed. The theory allows positive and negative charges of equal magnitude, where the sign of the charge corresponds to the chirality of the topological singularity. Given the trajectory of the singularity, one can calculate electric and magnetic fields identical to those produced by Maxwell's equations for a moving point charge, apart from a multiplicative constant factor related to electron charge and vacuum permittivity. The theory is based on the relativistic Weyl equation in frequency‐wavevector space, with eigenstates comprising the position, velocity, and acceleration of the singularity, and eigenvalues defining the retarded position of the charge. From the eigenstates, one calculates the Berry connection and the Berry curvatures, and identifies the curvatures as electric and magnetic fields.

Gravitational vacua in the Newman-Penrose formalism

In this paper, we derive the generic solution of the Newman-Penrose equations in the Newman-Unti gauge with vanishing curvature tensor. The obtained solutions are the vacua of the gravitational theory which are connected to the derivations in metric formalism from exponentiating the infinitesimal BMS generators in the Bondi-Metzner-Sachs (BMS) gauge in Compère and Long [ and ] by a radial transformation. The coordinate transformations in the Newman-Unti gauge connecting each vacuum are also obtained. We confirm that the supertranslation charge of the gravitational vacua with respect to global considerations vanishes exactly not only in the Einstein theory but also when including the Holst, Pontryagin, and Gauss-Bonnet terms, which verifies that the gravitational vacua are not affected by those trivial or boundary terms. Published by the American Physical Society 2024

New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gravity

We propose new slow-roll approximations for inflationary models with the Gauss-Bonnet term. We find more accurate expressions of the standard slow-roll parameters as functions of the scalar field. To check the accuracy of approximations considered we construct inflationary models with quadratic and quartic monomial potentials and the Gauss-Bonnet term. Numerical analysis of these models indicates that the proposed inflationary scenarios do not contradict to the observation data. New slow-roll approximations show that the constructed inflationary models are in agreement with the observation data, whereas one does not get allowed observational parameters at the same values of parameters of the constructed models in the standard slow-roll approximation.

Scalar field perturbation of hairy black holes in EsGB theory

We investigate scalar field perturbations of the hairy black holes involved with spontaneous symmetry breaking of the global U(1) symmetry in Einstein-scalar-Gauss-Bonnet theory for asymptotically flat spacetimes. We consider the mechanism that black holes without hairs become unstable at the critical point of the coupling constant and undergo a phase transition to hairy black holes in the symmetry-broken phase driven by spontaneous symmetry breaking. This transition occurs near the black hole horizon due to the diminishing influence of the Gauss-Bonnet term at infinity. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function, incorporating the branch cut contribution. This allows us to analytically investigate the late-time behavior of the perturbation at both spatial and null infinity. We found that the late-time behavior only differs from the Schwarzschild black hole by a mass term. We then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. Our primary interest lies in utilizing QNMs to investigate the stability of the black hole solutions both the symmetric and symmetry-broken phases. Consistent with the prior study, our analysis shows that hairy black holes in the symmetric phase become unstable when the quadratic coupling constant exceeds a critical value for a fixed value of the quartic coupling constant. In contrast, hairy black holes in the symmetry-broken phase are always stable at the critical value. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking.

General analysis of Noether symmetries in Horndeski gravity

We explore Noether symmetries of Horndeski gravity, extending the classification of general scalar–tensor theories. Starting from the minimally coupled scalar field and the first-generation scalar–tensor gravity, the discussion is generalised to kinetic gravity braiding and Horndeski gravity. We highlight the main findings by focusing on the non-minimally coupled Gauss–Bonnet term and the extended cuscuton model. Finally, we discuss how the presence of matter can influence Noether symmetries. It turns out that the selected Horndeski functions are unchanged with respect to the vacuum case.

Dynamics of a higher-dimensional Einstein–Scalar–Gauss–Bonnet cosmology

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann–Lemaître–Robertson–Walker metric in the context of a Gauss–Bonnet–Scalar field theory where the quintessence scalar field is coupled to the Gauss–Bonnet scalar. Contrary to the four-dimensional Gauss–Bonnet theory, where the Gauss–Bonnet term does not contribute to the field equations, in this five-dimensional Einstein–Scalar–Gauss–Bonnet model, the Gauss–Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe’s early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate.

Shear-free inhomogeneous energy density in 4D Einstein-Gauss-Bonnet spherical systems

We explore the inhomogeneity factors for the initially regular relativistic spheres in 4D-Einstein-Gauss-Bonnet (EGB) theory. The corresponding equations of motion are derived once the generic expressions for the kinematical variables are obtained for spherically symmetric self-gravitating system. By using the non-zero divergence of the stress-energy tensor, the independent components of Bianchi identities are constructed. To enable a thorough explanation of the inhomogeneity of the particular shear free matter distribution, we computed two distinct components of evolution equations employing the Weyl tensor. We then investigate the requisite variables for the irregularity by looking at particular scenarios in both the adiabatic and non-adiabatic domains. These instances demonstrate how, in addition to other factors, the Gauss-Bonnet terms contribute to the regularity requirements of the collapsing fluid.

Higgs inflation with a Gauss-Bonnet term

Higgs inflation with a Gauss-Bonnet term

Anisotropic stellar evolution and exotic matter

In this paper, we discuss the stability of isotropic pressure conditions for a spherically symmetric dissipative fluid distribution in the framework of f(G,T) gravity. We consider the fluid to be composed of seen and exotic matter particles. The Gauss Bonnet terms represent exotic matter particles. For the physical significance of the pressure isotropy conditions, we transform the system into the hydrostatic equilibrium approximation. We observe the presence of shear, dissipative fluxes, energy density inhomogeneities, and prominently, the exotic matter tends to abandon isotropy leading to pressure anisotropy. It is found that exotic matter and dissipation are major factors that induce matter anisotropy in the evolving stellar system. In order to discuss the physical significance of the stellar model in f(G,T) gravity, the behaviour of stellar structure is explored according to the observational data of a compact star 4U1820 − 30. It is found that f(G,T) terms indicating the exotic material in the stellar model plays a vital role in governing the dynamics of the evolution. To strengthen the results, we also incorporate some arguments by choosing an axially symmetric case.

Einstein-Gauss-Bonnet dark matter halo: negative masses, rotation curves and the origin of dark matter effects

This work presents a novel approach to address the longstanding challenge posed by the rotation curves of galaxies and the associated missing mass problem. Utilizing the four-dimensional modified gravity framework of Einstein-Gauss-Bonnet (EGB), we develop a new model that integrates the concept of dark matter featuring negative mass due to the Gauss-Bonnet term. Our methodology involves using the action of EGB with boundary terms to derive the Israel junction condition, allowing the formulation of a model featuring a spherical dark halo. The mass expression of this dark halo exhibits a remarkable proportionality to the radius r at large distances, forming the basis for subsequent analyses. The model’s implications extend to the dynamics of the early Universe, where we introduce a dynamic scalar field classified as Chameleon. Posting this scalar field as the origin of dark matter effects, we establish a crucial link between the coupling constant α and the scalar field through Z2 symmetry breaking via the effective potential. This connection enables a subtle description of velocity, reminiscent of Modified Newtonian Dynamics (MOND), providing insights into the gravitational interplay and dark matter dynamics. A pivotal aspect of our study involves a particular comparison of the model’s predictions with observational data sourced from SPARC datasets. The alignment of our theoretical outcomes with empirical evidence underscores the model’s efficiency and its potential contribution to our understanding of galactic rotation dynamics.

Cosmological time crystals from Gauss-Bonnet gravity in four dimensions

We investigate various cosmological aspects of a 4-Dimensional Gauss-Bonnet Lagrangian, which is integrated into the Einstein Lagrangian with an arbitrary sign, using the Friedman-Lemaître-Robertson-Walker (FLRW) metric. We consider a general potential term, V(a), that depends on the scale factor a, and we analyze several scenarios by investigating the critical points of the dynamical equations and stability conditions to understand how the universe's behavior is affected by the Gauss-Bonnet term. Our research suggests that choosing the negative sign, this integration allows for the spontaneous breaking of time reflection symmetry. This can lead to the generation of a wall-bounce universe even with a normal matter sector, marking a significant departure from traditional theories. Furthermore, we examine the possibility of a time-crystal universe, showing that under certain circumstances, the theory might give rise to cyclic universes.

Violation of Hod’s conjecture and probing it with optical properties of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity

In this work, the quasinormal modes of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity have been investigated with the help of the Padé averaged higher order WKB approximation method and the validity of Hod’s conjecture has been studied. It is found that the presence of Lorentz symmetry breaking due to the Bumblebee field favours Hod’s conjecture. But in the case of the Gauss–Bonnet term, an increase in the coupling parameter increases the chances of violation of Hod’s conjecture. We further investigated the optical properties of the black hole viz., shadow and emission rate. It is found that a black hole with a lower lifetime favours Hod’s conjecture.

Holographic renormalization of Horndeski gravity

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.

Probing Gauss-Bonnet-corrected inflation with gravitational waves

The low energy effective action of quantum gravity may include the higher curvature terms such as the Gauss-Bonnet term.The inflaton dynamics may be affected by the Gauss-Bonnet term if there is an inflaton-Gauss-Bonnet coupling.We show that an inflation model with a simple power law potential is made viable if it is coupled to the Gauss-Bonnet term since the prediction on the scalar spectral index and the tensor-to-scalar ratio are modified.We further point out that such a model predicts huge amount of gravitational waves at the high frequency range around 100 GHz–100 THz through the perturbative inflaton decay into gravitons induced by the Gauss-Bonnet term.Thus the spectrum of high frequency gravitational background is a unique feature of the inflation models with a Gauss-Bonnet correction.

Observational feasibility of 4D Einstein-Gauss-Bonnet cosmology: bouncing and non-bouncing universes

This paper analyzes the possibility of bouncing and non-bouncing universes in the framework of four-dimensional Einstein-Gauss-Bonnet (4D-EGB) gravity,corresponding respectively to negative and positive coupling constants λ of the Gauss-Bonnet term. We also use the Horndeski-type scalar-tensor theory to assess the role of a scalar charge C as a geometrical contribution to the radiation in the Universe.We modify the expansion history of the universe to allow for modifications induced by the 4D-EGB gravity.Using Planck measurements of the cosmic microwave background anisotropies as well as various datasets of baryonic acoustic oscillations, we set the upper bounds λ ≤ 10-16(km/s/Mpc)-2 and λ ≤ 10-30(km/s/Mpc)-2 for the non-bouncing and bouncing scenarios.The upper limit in the latter case is mainly driven by the requirement to conservatively respect the thermal history at energy scales of the standard model of particle physics.We also find that the contribution of the geometrical radiation-like term of the model cannot exceed 10% of the current radiation in the Universe. The possibility of an early inflationary phase produced by a single scalar field is also studied and found to be feasible in both bouncing and non-bouncing scenarios.This study shows the feasibility of a bouncing universe, even with a normal matter sector, in the 4D-EGB gravity. More theoretical investigation is required to further explore possible observational predictions of the model that can distinguish between general relativity and 4D-EGB gravity.