Einstein Gauss Bonnet Research Articles

Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields

In this paper, we investigate the time dependent black holes in the frame of Einstein–Gauss–Bonnet theory having two scalar fields and investigate the propagation of the gravitational wave (GW). In the reconstructed models, there often appear ghosts, which could be eliminated by imposing some constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss–Bonnet coupling during their propagation. The speed of propagation changes due to the coupling during the black hole formation process. The propagation speed of gravitational waves differs when they enter the black hole compared to when they exit.

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.

Magnetic black holes in 4D Einstein–Gauss–Bonnet massive gravity coupled to nonlinear electrodynamics

We investigated Einstein–Gauss–Bonnet (EGB) 4D massive gravity coupled to nonlinear electrodynamics (NED) in an anti-de Sitter (AdS) background and found an exact magnetically charged black hole solution. The metric function was analyzed for different values of massive gravity parameters. The first law of black hole thermodynamics and generalized Smarr formula were verified, where we treated the cosmological constant as thermodynamic pressure. We defined vacuum polarization as the conjugate to NED parameter. To analyze the local stability of the black hole, we computed specific heat. We investigated the van der Waals-like/re-entrant phase transition of the black holes and estimated the critical points. We observed small black hole (SBH)/large black hole (LBH) and SBH/intermediate black hole (IBH)/LBH phase transitions. The Joule–Thomson coefficient, inversion, and isenthalpic curves were discussed. Finally, the minimum inversion temperature and the corresponding event horizon radius were obtained using numerical techniques.

Casimir wormholes inspired by electric charge in Einstein–Gauss–Bonnet gravity

This investigation assesses the feasibility of a traversable wormhole by examining the energy densities associated with charged Casimir phenomena. We focus on the influence of the electromagnetic field created by an electric charge as well as the negative energy density arising from the Casimir source. We have developed different shape functions by defining energy densities from this combination. This paper explores various configurations of Casimir energy densities, specifically those occurring between parallel plates, cylinders and spheres positioned at specified distances from each other. Furthermore, the impact of the generalized uncertainty principle correction is also examined. The behavior of wormhole conditions is evaluated based on the Gauss–Bonnet coupled parameter (μ) and electric charge (Q) through the electromagnetic energy density constraint. This is attributed to the fact that the electromagnetic field satisfies the characteristic ρ = −p r . Subsequently, we examine the active gravitational mass of the generated wormhole geometries and explore the behavior of μ and Q concerning active mass. The embedding representations for all formulated shape functions are examined. Investigations of the complexity factor of the charged Casimir wormhole have demonstrated that the values of the complexity factor consistently fall within a particular range in all scenarios. Finally, using the generalized Tolman–Oppenheimer–Volkoff equation, we examine the stability of the resulting charged Casimir wormhole solutions.

Charged AdS black holes with higher derivative corrections in the presence of string cloud

We have obtained charged asymptotically anti-de Sitter (AdS) black hole solutions in Einstein–Gauss–Bonnet gravity in the presence of string cloud. It turns out that there exist three black holes in certain range of parameters for small enough chemical potential. However, for large chemical potential, these black holes merge into a single one. The free energy of the black holes is computed from the on-shell Euclidean action by subtracting the contribution of an extremal black hole. We have studied the free energy and specific heat of the solutions, which shows that the medium-sized black hole is unstable. As an application, we have studied the quark–antiquark potential in the dual gauge theory. This study provides necessary ingredients for the study of the dual theories in the context of condensed matter systems.

Thermodynamics, phase transition and Joule–Thomson expansion of 4-D Gauss–Bonnet AdS black hole

In this paper, we explore the thermodynamic and phase transition properties of asymptotically AdS black holes within Einstein–Gauss–Bonnet gravity, focusing on Joule–Thomson expansion. Thermodynamics is studied in the extended phase space, where the cosmological constant serves as thermodynamic pressure. We observe that the black hole undergoes a phase transition similar to that of a van der Waals system. We analyze charged and neutral cases separately to distinguish the effect of charge and Gauss–Bonnet parameter on critical behavior and examine the phase structure. We find that the Gauss–Bonnet coupling parameter behaves similarly to black hole charge or spin, guiding the phase structure. To understand the underlying phase structure determined by the Gauss–Bonnet coefficient [Formula: see text], we introduce a new order parameter. We discover that the change in the conjugate variable to the Gauss–Bonnet parameter acts as an order parameter, demonstrating a critical exponent of [Formula: see text] in the vicinity of the critical point. Since the phase structure is analogous to that of a van der Waals fluid, we investigate the Joule–Thomson expansion of the black hole. We analytically study the Joule–Thomson expansion, focusing on three key characteristics: the Joule–Thomson coefficient, inversion curves and isenthalpic curves. We obtain isenthalpic curves in the T–P plane and illustrate the cooling–heating regions.

Perturbing the Stable Accretion Disk in Kerr and 4D Einstein–Gauss–Bonnet Gravities: Comprehensive Analysis of Instabilities and Dynamics

The study of a disturbed accretion disk holds great significance in the realm of astrophysics, as such events play a crucial role in revealing the nature of disk structure, the release of energy, and the generation of shock waves. Consequently, they can help explain the causes of X-ray emissions observed in black hole accretion disk systems. In this paper, we perturb the stable disk formed by spherical accretion around Kerr and Einstein–Gauss–Bonnet (EGB) black holes. This perturbation reveals one- and two-armed spiral shock waves around the black hole. We find a strong connection between these waves and the black hole spin parameter (a/M) and the EGB coupling constant (α). Specifically, we find that as α increases in the negative direction, the dynamics of the disk and the waves become more chaotic. Additionally, we observe that the angular momentum of the perturbing matter significantly affects mass accretion and the oscillation of the arising shock waves. This allows us to observe changes in QPO frequencies, particularly, perturbations with angular momentum matching the observed C−type low-frequency QPOs of the GRS 1915+105 source. Thus, we conclude that the possibility of the occurrence of shock waves within the vicinity of GRS 1915+105 is substantial.

Traversable wormholes in 4D EGB gravity

In this work, the spherically symmetric wormhole solutions have been obtained in the four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity with isotropic and anisotropic matter sources. With each type of source, the traversable wormholes satisfying asymptotic flatness and flare-out conditions are developed. Further, the energy conditions explaining the nature of the matter in the interior of the wormhole are tested and the stability of wormhole solutions has been analyzed.

Extremely small stars in scalar-tensor gravity: When stellar radius is less than Schwarzschild one

We show analytically that there exist compact stellar objects akin to neutron stars whose radius is smaller than the Schwarzschild radius defined by Arnowitt-Deser-Misner (ADM) mass. The radius of the compact object is defined by the radius where the energy density and the pressure of ordinary matter vanish, while clouds of scalar(s) can extend beyond this radius – a situation that is often encountered in modified gravity theories, like F(R) gravity and the scalar–Einstein–Gauss-Bonnet gravity. The clouds of scalar mode(s) give additional contributions to the ADM mass and as a result, the corresponding Schwarzschild radius given by the ADM mass can be larger than that of the compact object.

Possibility of the Traversable Wormholes in the Galactic Halos within 4D Einstein–Gauss–Bonnet Gravity

AbstractRecently, there has been significant interest regarding the regularization of a limit of Einstein–Gauss–Bonnet (EGB) gravity. This regularization involves re‐scaling the Gauss–Bonnet (GB) coupling constant as , which bypasses Lovelock's theorem and avoids Ostrogradsky instability. A noteworthy observation is that the maximally or spherically symmetric solutions for all the regularized gravities coincide in the scenario. Considering this, the wormhole solutions in the galactic halos are investigated based on three different choices of dark matter (DM) profiles, such as Universal Rotation Curve, Navarro–Frenk–White, and Scalar Field Dark Matter with the framework of EGB gravity. Also, the Karmarkar condition is used to find the exact solutions for the shape functions under different non‐constant redshift functions. The energy conditions for each DM profile are discussed and the influence of GB coefficient in violating energy conditions are noticed, especially null energy conditions. Further, some physical features of wormholes, viz. complexity factor, active gravitational mass, total gravitational energy, and embedding diagrams, have been explored.

4D Einstein–Gauss–Bonnet cosmology with Chameleon mechanism

4D Einstein–Gauss–Bonnet cosmology with Chameleon mechanism

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.

The role of topological photon spheres in constraining the parameters of black holes

In this paper, we investigate the topological photon sphere from two distinct perspectives. In the first view, we examine the existence and characteristics of topological photon (anti-photon) spheres for black holes with different structures, such as Einstein–Young–Mills non-minimal, AdS black holes surrounded by Chaplygin-like dark fluid, and Bardeen-like black holes in Einstein–Gauss–Bonnet gravity. Furthermore, we delve into the deeper perspective of the necessity of photon spheres for super-compact gravitational structures such as black holes. By leveraging this necessity, we propose a classification of the parameter space of black hole models based on the existence and positioning of photon spheres. This approach enables the determination of parameter ranges that delineate whether a solution represents a black hole or a naked singularity. In essence, the paper illustrates the utility of the photon sphere as a notable test for establishing the permissible and non-permissible parameter ranges within specific theories of black hole solutions.

The comparison of alternative spacetimes using the spherical accretion around the black hole

In the region where the gravitational field is strong, we have examined the influence of different gravities on the accretion disk formed due to spherical accretion. To achieve this, we obtain numerical solutions of the GRH equations, utilizing Schwarzschild, Kerr, Einstein–Gauss–Bonnet, and Hartle–Thorne spacetime metrics. We investigate the impact of the rotation parameter of a black hole ([Formula: see text]), the EGB coupling constant ([Formula: see text]), and the quadrupole moment of the rotating black hole (q) on the accretion disk formed in a strong field. The formation of the disk for the slowly and rapidly rotating black hole models is separately examined, and comparisons are made. Our numerical simulations reveal that, under the specific conditions, the solution derived from Hartle–Thorne gravity converges toward solutions obtained from Kerr and other gravitational models. In the context of the slowly rotating black hole with [Formula: see text], we observe a favorable agreement between the Hartle–Thorne result and the Kerr result within the range of [Formula: see text]. Conversely, in the scenario of the rapidly rotating black hole, a more pronounced alignment with the value of [Formula: see text] is evident within the range of [Formula: see text]. Nevertheless, for [Formula: see text], it becomes apparent that the Hartle–Thorne solution diverges from solutions provided by all gravitational models. Our motivation here is to utilize the Hartle–Thorne spacetime metric for the first time in the numerical solutions of the GRH equations for the black holes, compare the results with those obtained using other gravities, and identify under which conditions the Hartle–Thorne solution is compatible with known black hole spacetime metric solutions. This may allow us to provide an alternative perspective in explaining observed X-ray data.

Extended phase space thermodynamics of Bardeen–Letelier black holes in 4D Einstein–Gauss–Bonnet gravity

Extended phase space thermodynamics of Bardeen–Letelier black holes in 4D Einstein–Gauss–Bonnet gravity

Propagation of gravitational waves in a dynamical wormhole background for two-scalar Einstein–Gauss–Bonnet theory

In this work, we propose a model of Einstein–Gauss–Bonnet gravity coupled with two scalar fields. The two scalar fields are considered to be “frozen” or they become non-dynamical by employing appropriate constraints in terms of Lagrange multiplier fields. We show that, even in the case that the arbitrary spherically symmetric spacetime is dynamical, we can construct a model where the wormhole spacetime is a stable solution in this framework. We especially concentrate on the model reproducing the dynamical wormhole, where the wormhole appears in a finite-time interval. We investigate the propagation of the gravitational wave in the wormhole spacetime background and we show that the propagation speed is different from that of light in general, and there is a difference in the speeds between the incoming propagating wave and the outgoing propagating gravitational wave. We need to stress that the wormhole model used for exploring gravitational wave propagation is not obtained by solving any equations but is essentially constructed by hand.

Black holes in degenerate Einstein Gauss-Bonnet gravity: can QNMs distinguish them from GR?

For the first time, we study the quasi-normal modes(QNMs) of massless scale fields propagating in spacetimes with zero metric determinant. In this context, we work with asymptotically flat solutions to degenerate Einstein-Gauss-Bonnet (EGB) theory introduced in [JCAP 02 (2022) 020]. This solution has two distinct branches akin to Einstein Gauss-Bonnet(EBG) gravity. However, unlike the EBG solutions, both the branches of dEGB are well-defined asymptotically. The negative branch solutions from both theories are equivalent under the identification of certain parameters. We provide constraints on the Gauss-Bonnet coupling parameters, which result in black hole spacetimes, and study the behaviour of a propagating scalar field through the computation of QNMs. Finally, we compare the time domain evolution of the scalar field in the background of these black holes with their GR counterparts.

Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: Constraints from supermassive black holes

Observation indicates that many nearby galaxies host supermassive central black holes. We use the Bardeen black holes in four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity, with additional parameters-the coupling constant α̃ and charge q, as central black holes in various galaxies to investigate gravitational lensing properties in strong field regime. Taking the supermassive black holes Sgr A* and M87* as the lens, we compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. In the case of 4D EGB Bardeen black holes we observed that he angular position θ∞ for Sgr A* ∈ (23.19, 25.56) μ as, whereas for M87* it is ∈ ( 17.94,19.78) μ as. Further, the angular separation s, which is an increasing function of α̃ and q for Sgr A* and M87* differs significantly, respectively, in (0.032, 0.15) μ as and (0.025, 0.115) μ as. The deviations of the lensing observables Δθ∞ and Δs for 4D EGB Bardeen black hole (α̃=0.9,q=0.09) from the Schwarzschild black hole, respectively, can reach up to 2.38μ as and 0.12μ as for Sgr A* , 1.84μ as and 0.09μ as for M87*. On the other hand, the relative magnification ∈ (4.66,6.82). Considering twenty-one massive central black holes as lens, we also estimate the time delay ΔT2,1s between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach ∼9.86 min and ∼16023.93 min. We also show that the existing shadow size measurements place strong constraints on the parameters considered Bardeen model. This combination of gravitational lensing and EHT results may complement comprehensive restrictions on modifications of the general relativity.

The role of dimension and electric charge on a collapsing geometry in Einstein–Gauss–Bonnet gravity

The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximum electric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnet gravity as well as general relativity. The charged gravitational collapse process is also similar for all dimensions N≥5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\\ge 5$$\\end{document} unlike in the neutral scenario where there is a marked difference between the N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} and N>5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N>5$$\\end{document} cases. In the case where N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, before succumbing to an event horizon. The similarity of charged collapse for all higher dimensions is a unique feature in the theory. The sufficient conditions for the formation of a naked singularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein–Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested and it is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible.

The Shock Cone Instabilities and Quasi-Periodic Oscillations around the Hartle–Thorne Black Hole

To explain the observed X-ray data in a black hole–accreting matter system and understand the physical mechanisms behind QPOs, we have numerically modeled the dynamical and oscillation properties of the shock cone formed around both slowly and rapidly rotating Hartle–Thorne black holes, resulting from the mechanism of Bondi–Hoyle–Lyttleton (BHL). According to the numerical simulations, an increase in the quadrupole parameter leads to a decrease in the shock cone opening angle around the black hole. A larger quadrupole parameter results in more matter falling into the black hole within the cone. The combination of the quadrupole parameter and black hole rotation causes the matter inside the cone to exhibit chaotic motion. These dynamical changes and chaotic behavior of the shock cones excite the fundamental oscillation modes. Moreover, new frequencies have been formed due to the nonlinear coupling of the fundamental modes. Conversely, we have numerically studied the behavior of cones formed around rapidly rotating Hartle–Thorne black holes and found differences and similarities to those obtained from slowly rotating cases. Finally, comparing the outcomes obtained fromHartle–Thorne gravity with the results fromKerr and Einstein–Gauss–Bonnet (EGB) gravities reveals the impact of the quadrupole parameter on the shock cone and QPOs.