4D Einstein Gauss Bonnet Gravity Research Articles

Quasi-periodic oscillation around regular Bardeen black holes in 4D Einstein–Gauss–Bonnet gravity

In this paper, we explore the dynamics of test particles in spacetime around regular Bardeen black holes (BHs) in the novel four-dimensional Einstein–Gauss–Bonnet (4D EGB) theory. First, we analyze properties of the spacetime around the Bardeen BH with respect to the Gauss–Bonnet (GB) coupling parameter [Formula: see text], and we show the range of values of the BH charge and the parameter [Formula: see text] that horizon exists as [Formula: see text] and [Formula: see text], respectively. We also investigate the effects of the magnetic charge of the regular BH on innermost stable circular orbits (ISCOs) radius and efficiency of energy release from infalling test particles to the regular Bardeen BH in 4D EGB gravity. Moreover, fundamental frequencies such as Keplerian and harmonic oscillations are also studied with the applications of quasi-periodic oscillations (QPOs) where we proposed a method to test gravity theories through data from astrophysical observations of twin-peak QPOs in relativistic precession (RP) model. Finally, we show the dependence of the distance from the central BH to the orbit where twin-peak QPOs shine from the spin of Kerr BH, magnetic charge of Bardeen and Reissner–Nordström (RN) BHs, and GB coupling parameter.

Charged black holes in 4D Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics with maximum allowable symmetries

Recently a new model of nonlinear Maxwell electrodynamics which preserves both conformal and SO(2) duality-rotational invariance has been proposed. In this work, we consider this model as a source of gravitational field and study black holes of novel four-dimensional Einstein–Gauss–Bonnet gravity. In this framework we solve the gravitational field equations and work out the metric function that describe a black hole which generalizes the Maxwellian charged black hole of four-dimensional Einstein–Gauss–Bonnet gravity. Some basic thermodynamic quantities corresponding to the new black hole solution are computed and thermodynamic stability as well as thermal phase transitions are investigated.

New Model of 4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics

New spherically symmetric solution in 4D Einstein–Gauss–Bonnet gravity coupled with nonlinear electrodynamics is obtained. At infinity, this solution has the Reissner–Nordström behavior of the charged black hole. The black hole thermodynamics, entropy, shadow, energy emission rate, and quasinormal modes of black holes are investigated.

Einstein–Gauss–Bonnet Gravity with Nonlinear Electrodynamics: Entropy, Energy Emission, Quasinormal Modes and Deflection Angle

The logarithmic correction to Bekenshtein–Hawking entropy in the framework of 4D Einstein–Gauss–Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics

A new exact spherically symmetric and magnetically charged black hole solution in regularization scheme of Glavan and Lin is obtained. The nonlinear electrodynamics Lagrangian is given by LNED=−F/(1+2βF4), where F is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radius is calculated and we study its dependance on model parameters.

Color–flavor locked strange stars in 4D Einstein–Gauss–Bonnet gravity

This work is devoted to the recently introduced Einstein–Gauss–Bonnet gravity in four dimensions. This theory can bypass Lovelock’s theorem and avoids Ostrogradsky instability. The integrated part of this theory is the GB term which gives rise to a non-trivial contribution to the gravitational dynamics in the limit D→4. Our main interest is to explore a class of static, spherically symmetric compact objects made of strange matter. It is believed that at ultra-high densities, quark matter may exist in a variety of superconducting states, namely, the Color–Flavor-Locked (CFL) phase. With these equations of state (EoS) we explore the conditions under which compact stars are stable under extreme conditions in the context of 4D EGB gravity. In addition, the mass–radius relation is examined and the effects of the coupling constant ‘α’ on the stellar model, energy conditions, speed of sound and adiabatic stability are studied. With the aim to find observational constraints on the GB constant of 4D EGB gravity, the mass–radius curve is determined satisfying the maximum mass constraint of M∼2M⊙ for neutron stars. This feature may be relevant in view of recent observations claiming the existence of stable compact quark stars (hybrid neutron stars or strange stars).

Quark Stars in 4D Einstein–Gauss–Bonnet Gravity with an Interacting Quark Equation of State

Abstract The detection of gravitational waves (GWs) from a binary neutron star (BNS) has opened a new window on gravitational wave astronomy. With current sensitivities, detectable signals coming from compact objects like neutron stars turn out to be a crucial ingredient for probing their structure, composition, and evolution. Moreover, astronomical observations on pulsars and their mass–radius relations place important constraints on the dense matter equation of state. In this paper, we consider a homogeneous and unpaired charge-neutral three-flavor interacting quark matter with corrections that account for the moderately heavy strange quark instead of the naive MIT bag model. We perform a detailed analysis of strange quark stars in the context of the recently proposed 4D Einstein–Gauss–Bonnet (EGB) theory of gravity. However, this theory does not have standard 4D equations. Thus, we show that the equivalence of the actions in the regularized 4D EGB theory and in the original one is satisfied for a spherically symmetric spacetime. We pay particular attention to the possible existence of neutron stars of mass compatible with . Our findings suggest that the fourth-order correction parameter (a 4) of the quantum chromodynamic perturbation and coupling constant α of the GB term play an important role in the mass–radius relation as well as the stability of the quark star. Finally, we compare the results with the well-measured limits of pulsars and their mass and radius extracted from the spectra of several X-ray compact sources.

Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics

Einstein–Gauss–Bonnet (EGB) gravity is an outcome of quadratic curvature corrections to the Einstein–Hilbert gravity action in the form of a Gauss–Bonnet (GB) term in D>4 dimensions and EGB gravity is topologically invariant in 4D. Recently several ways have been proposed for regularizing, a D→4 limit of EGB, for nontrivial gravitational dynamics in 4D. Motivated by the importance of anti-de Sitter gravity/conformal field theory correspondence (AdS/CFT), we analyse black holes with AdS asymptotic of regularized 4D EGB gravity coupled to the nonlinear electrodynamics (NED) field. For a static spherically symmetric ansatz the field equations are solved exactly, using two different approaches, for a NED Lagrangian to obtain an identical solution−namely NED charged AdS black holes in 4D EGB gravity which retains several known solutions. Owing to the NED charge corrected EGB black holes, the thermodynamic quantities are also modified, and the entropy does not obey the usual area law. We calculate the heat capacity and Helmholtz free energy, in terms of horizon radii, to investigate both local and global thermodynamic stability of black holes. We observe a secondary Hawking–Page transition between the smaller thermally favoured black hole and thermal AdS space. Our results show that the behaviour of Hawking’s evaporation abruptly halts at shorter radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.

Generating black holes in 4D Einstein–Gauss–Bonnet gravity

In recent times there is a surge of interest in constructing Einstein–Gauss–Bonnet (EGB) gravity, in the limit D → 4, of the D-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed D → 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 proof as being similar to the original theorem, generates static spherically symmetric black hole solutions of the theory. It not only enables us to identify available known black hole solutions as particular cases but also to generate several new solutions of the 4D EGB gravity.

Quasinormal modes of the Dirac field in the consistent 4D Einstein–Gauss–Bonnet gravity

Recently a consistent well-defined 4-dimensional Einstein–Gauss–Bonnet theory of gravity was suggested in [K. Aoki, M. Gorji and S. Mukohyama, Phys. Lett. B 810, 135843 (2020)]. While quasinormal modes of bosonic fields for this theory have been recently studied, there is no such study for fermionic fields. Here we calculate quasinormal modes of the Dirac field for spherically symmetric asymptotically flat black hole in this consistent 4D Einstein–Gauss–Bonnet theory. The values of the quasinormal frequencies, calculated by the sixth order WKB method with Padé approximants and the time-domain integration, show that the real part of the quasinormal modes is considerably increased, while the damping rate is usually decreasing when the coupling constant is growing.

Quasinormal modes and strong cosmic censorship in the regularised 4D Einstein–Gauss–Bonnet gravity

The fate of strong cosmic censorship is ultimately linked to the extendibility of perturbation across the Cauchy Horizon and known to be violated in the near extremal region of a charged de Sitter black hole. Similar violations can also be realized in higher curvature theories, with the strength of violation becoming stronger as compared to general relativity. In this work, we extend this analysis further to study the validity of strong cosmic censorship conjecture in the context of the regularised four-dimensional Einstein Gauss-Bonnet theory with respect to both scalar and electromagnetic perturbation. We also study the late time tails of scalar fields.

Growth of matter density perturbations in 4D Einstein–Gauss–Bonnet gravity

Recently, a novel Einstein-Gauss-Bonnet gravity in four dimensions has been introduced [Phys. Rev. Lett. 124 (2020) 081301]. We will investigate cosmological consequences of this model in details. We will consider linear matter density perturbations and also estimate relevant modified gravity parameters. Specially we will concentrate on the growth rate of non-relativistic matter perturbations on top of FRW geometry and show that for a narrow range of the Gauss-Bonnet coupling constant, observational data will be satisfied. In this paper, it is shown that for enough large values of the coupling constant, the suggested $\sigma_8$ will become greater than $\Lambda$CDM value.

On causal structure of 4D-Einstein\u2013Gauss\u2013Bonnet black hole

The recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in Dge 5, the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.

Nonlinear magnetically charged black holes in 4D Einstein–Gauss–Bonnet gravity

In this letter we present an exact spherically symmetric and magnetically charged black hole solution with exponential model of nonlinear electrodynamics (Kruglov, 2017) in the context of 4D Einstein–Gauss–Bonnet (EGB) gravity. We show that our −ve branch, in the limit of GB coupling coefficient α→0 and the nonlinear parameter β→0, reduces to the magnetically charged black hole of Einstein–Maxwell gravity in GR. In addition we study the embedding diagram of the black hole geometry and the thermodynamic properties such as the Hawking temperature and the heat capacity of our black hole solution.

A note on the novel 4D Einstein–Gauss–Bonnet gravity

Recently, a novel 4D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin (2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling and taking the limit at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit in the higher D-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the 4D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in (2020 Phys. Rev. Lett. 124 081301).

Radiating black holes in the novel 4D Einstein–Gauss–Bonnet gravity

Recently Glavan and Lin (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→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→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 rEH<rAH=rTLS. The charged radiating black holes in the theory, generalizing Bonnor–Vaidya black holes, are also considered. In particular our results, in the limit α→0, reduced exactly to vis-à-vis 4D black holes of GR.

Rotating black holes in 4D Einstein-Gauss-Bonnet gravity and its shadow

Recently there has been a surge of interest in regularizing, a D → 4 limit of, the Einstein-Gauss-Bonnet (EGB) gravity, and the resulting regularized 4D EGB gravity has nontrivial dynamics. The theory admits spherically symmetric black holes generalizing the Schwarzschild black holes. We consider the rotating black hole in regularized 4D EGB gravity and discuss their horizon properties and shadow cast. The effects of the GB coupling parameter on the shape and size of shadows are investigated in the context of recent M87* observations from the EHT . Interestingly, for a given spin parameter, the apparent size of the shadow decreases and gets more distorted due to the GB coupling parameter. We find that within the finite parameter space, e.g. for a=0.1M, α⩽ 0.00394M2, and within the current observational uncertainties, the rotating black holes of the 4D EGB gravity are consistent with the inferred features of M87* black hole shadow.

Dust collapse in 4D Einstein–Gauss–Bonnet gravity

We consider gravitational collapse in the recently proposed 4D limit of Einstein-Gauss-Bonnet gravity. We show that for collapse of a sphere made of homogeneous dust the process is qualitatively similar to the case of pure Einstein's gravity. The singularity forms as the endstate of collapse and it is trapped behind the horizon at all times. However, and differently from Einstein's theory, as a consequence of the Gauss-Bonnet term, the collapsing cloud reaches the singularity with zero velocity, and the time of formation of the singularity is delayed with respect to the pure Einstein case.

Charged black holes in AdS spaces in 4D Einstein Gauss-Bonnet gravity

Recently a non-trivial 4-dimensional theory of gravity that claims to circumvent Lovelock's theorem and avoid Ostrogradsky instability was formulated in Glavan and Lin (2020) [1]. This theory, named “4D Einstein Gauss-Bonnet gravity”, presents several novel predictions for cosmology and black hole physics. In this paper, we generalize the vacuum black hole solution of Glavan & Lin to include electric charge in an anti-de Sitter space and explore some properties of this solution such as the asymptotics, properties of the horizons, the general relativity limit and thermodynamics.