Gauss-Bonnet Gravity Research Articles

Testing viable extensions of Einstein–Gauss–Bonnet gravity

Some models within the framework of Gauss–Bonnet gravities are considered in the presence of a non-minimally coupled scalar field. By imposing a particular constraint on the scalar field coupling, a class of these theories called Einstein–Gauss–Bonnet gravity keeps the correct speed of propagation for gravitational waves. The cosmological evolution for this viable class of models is studied and compared with observational data (BAO, CMB, Sne Ia,..), where we obtain the corresponding bounds for these theories and show that such theories fit well the data and provide a well-behaved cosmological evolution in comparison to the standard model of cosmology. Some statistical parameters show that the goodness of the fits are slightly better than those for Λ CDM model.

Generalized entropy increase at linear order in general second-order scalar-tensor gravity

Although the Wald entropy is commonly suitable for the first law of black hole thermodynamics, whether it satisfies the second law has not been examined sufficiently. For any high-order curvature gravity, the Wald entropy has been shown not to obey the linearized second law, and the general expression of entropy of black holes that always satisfies the linearized second law is further obtained. For gravity with nonminimal coupling matter fields, however, whether the Wald entropy of black holes satisfies the second law has not been studied enough. Recently, a general second-order scalar-tensor gravitational theory has been proposed. The Lagrangian of the gravitational theory is a linear combination of four components, and the Wald entropy can also be written as four parts. We should investigate each part of the expression separately to examine whether the Wald entropy satisfies the linearized second law. For the first and fourth parts contributed by two nonminimal coupling terms in Lagrangian contained in Horndeski gravity and Gauss-Bonnet gravity, the entropy of black holes is not expressed as the Wald entropy because the entropy in Gauss-Bonnet gravity is Jacobson-Myers entropy. The third part contributed by the Lagrangian in Einstein-Hilbert action is Bekenstein-Hawking entropy, which obeys the second law automatically. Therefore, to obtain the entropy of black holes that meets the linearized second law, we only need to study the second part of the Wald entropy. According to the null energy condition and the Raychaudhuri equation, one can show that the second part of the Wald entropy with correction terms will increase monotonically constrained by the null energy condition during the perturbation process. The second part of the Wald entropy should be modified to satisfy the linearized second law, and the expression of the entropy of black holes, which always obeys the linearized second law, is obtained in the general second-order scalar-tensor gravity.

Reheating era in Gauss-Bonnet theories of gravity compatible with the GW170817 event

In the present article we showcase how the reheating era can be described properly in the context of Einstein-Gauss-Bonnet gravity assuming that the primordial gravitational waves propagate with the velocity of light. The equations of the duration of reheating along with the reheating temperature are derived and as demonstrated, their expressions are quite similar to the case of a canonical scalar field where now the second derivative of the Gauss-Bonnet scalar coupling function appears and effectively alters the numerical value of the scalar potential. The appearance of such term is reminiscing of a λR model of gravity where λ is now dynamical. We consider two viable inflationary models of interest, the former involves an error function as scalar Gauss-Bonnet coupling function and the latter a Woods-Saxon scalar potential. It is shown that for both models the aforementioned quantities can be in agreement with theoretical expectations. The only constraint that is needed is the assumption that the second time derivative of the Gauss-Bonnet scalar coupling function is actually lesser than the Planck mass squared, that is ξ¨<MPl28 in order to obtain a viable description. We find that a free parameter of the theory and specifically the potential amplitude for the Woods-Saxon model during the inflationary era, dictates the effective equations of state and therefore the reheating epoch can be described either by a type of stiff matter with EoS parameter equal to unity or by an EoS parameter close to that of the radiation.

Gravitational collapse in Einstein-Gauss-Bonnet gravity

The Einstein- Gauss- Bonnet (EGB) gravity is an important modification of the Einstein theory of gravity and, for many gravitational phenomena, the Gauss- Bonnet (GB) correction term leads to drastic differences. In this paper, we study gravitational collapse in the $5$-dimensional EGB theory. We construct the spherical marginally trapped surfaces and determine the evolution of marginally trapped surfaces when the infalling matter admits a wide variety of initial density distribution. We show that the location of black hole horizon depends crucially on the initial density and velocity profile of the inflating matter as well as on the GB coupling constant. A detailed comparison is made with the results of Einstein's theory.

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss–Bonnet gravity: from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small–large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small–large black hole phase transition. For the six-dimensional charged Gauss–Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure–temperature and temperature–horizon radius diagrams. Quite different from the liquid–vapor phase transition, a double peak behavior is present in the temperature–horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss–Bonnet gravity.

Multihorizons black hole solutions, photon sphere, and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity

Among the modified gravitational theories, the ghost-free Gauss-Bonnet (GFGB) theory of gravity has been considered from the viewpoint of cosmology. The best way to check its applicability could be to elicit observable predicts which give guidelines or limitations on the theory, which could be contrasted with the actual observations. In the present study, we derive consistent field equations for GFGB and by applying the equations to a spherically symmetric space-time, we obtain new spherically symmetric black hole (BH) solutions. We study the physical properties of these BH solutions and show that the obtained space-time possesses multihorizons and the Gauss-Bonnet invariants in the space-time are not trivial. We also investigate the thermodynamical quantities related to these BH solutions and we show that these quantities are consistent with what is known in the previous works. Finally, we study the geodesic equations of these solutions which give the photon spheres and we find the perihelion shift for weak GFGB. In addition, we calculate the first-order GFGB perturbations in the Schwarzschild solution and new BH solutions and show that we improve and extend existing results in the past literature on the spherically symmetric solutions.

Quasibound states of scalar fields in the consistent 4D Einstein–Gauss–Bonnet–(Anti-)de Sitter gravity

We examine the interaction between massless scalar fields and the gravitational field generated by a black hole solution that was recently obtained in the consistent well-defined 4-dimensional Einstein–Gauss–Bonnet gravity with a cosmological constant. In order to do this, we calculate quasibound state frequencies of scalar fields for the spherically symmetric black hole in the consistent 4-dimensional Einstein–Gauss–Bonnet–de Sitter and Anti-de Sitter theories. The expression for the quasibound states is obtained by using the polynomial condition associated to the Heun functions, and their values are overdamped. We also demonstrate the stability of the systems.

Chaos in quadratic gravity

While recent gravitational wave observations by LIGO and Virgo allow for tests of general relativity in the extreme gravity regime, these observations are still blind to a large swath of phenomena outside these instruments' sensitivity curves. Future gravitational-wave detectors, such as LISA, will enable probes of longer-duration and lower-frequency events. In particular, LISA will enable the characterization of the non-linear dynamics of extreme mass-ratio inspirals, when a small compact object falls into a supermassive black hole. In this paper, we study the motion of test particles around spinning black holes in two quadratic gravity theories: scalar Gauss-Bonnet and dynamical Chern-Simons gravity. We show that geodesic trajectories around rotating black holes in these theories are likely to not have a fourth constant of the motion. In particular, we show that Poincar\'e sections of the orbital phase space present chaotic features that will affect the inspiral of small compact objects into supermassive black holes in these theories. Nevertheless, the characteristic size of these chaotic features is tiny and their location in parameter space is very close to the event horizon of the supermassive black hole. Therefore, the detection of such chaotic features with LISA is likely very challenging, at best.

Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity

In regularized 4-dimensional Einstein-Gauss-Bonnet (EGB) gravity derived from a Kaluza-Klein reduction of higher-dimensional EGB theory, we study the existence and stability of black hole (BH) solutions on a static and spherically symmetric background. We show that asymptotically-flat hairy BH solutions realized for a spatially-flat maximally symmetric internal space are unstable against linear perturbations for any rescaled GB coupling constant. This instability is present for the angular propagation of even-parity perturbations both in the vicinity of an event horizon and at spatial infinity. There is also a strong coupling problem associated with the kinetic term of even-parity perturbations vanishing everywhere.

Dynamics of scalar hair with self-interactions around a Schwarzchild black hole

In this paper, we study the dynamics of scalar hair around a Schwarzchild black hole. The scalar hair is sourced by the Gauss-Bonnet invariant with a linear coupling. We work perturbatively in the coupling constant and ignore the backreaction of the scalar hair and the Gauss-Bonnet invariant. We evolve the scalar field in the background of a Schwarzchild black hole and study the dynamical formation of scalar hair with different self-interactions. We integrate the energy and compute the energy flux of the scalar hair in terms of the canonical energy-momentum tensor and give the corresponding dependence on the self-interactions. Our results allow us to estimate the radiation and the condensation of scalar field with different self-interactions; these would improve our understanding for the dynamical scalarization of black holes and the possible configuration of the scalar hair in scalar Gauss-Bonnet gravity.

Black Hole Shadows Constrain Extended Gravity

The first images of black hole shadows open new possibilities to constrain modern extended gravity theories. We present the method of shadow background calculation for black hole solutions in the form of Taylor series where $g_{11} = - g_{00}^{-1}$. The method is extended to general non-rotating case $g_{11} \neq - g_{00}^{-1}$. The results of the analysis are compared with the predictions of General relativity taking into account the Event Horizon Telescope data. The results for the Horndesky model with the Gauss-Bonnet invariant, loop quantum gravity, Bumblebee model and Gauss-Bonnet gravity are in full agreement with the observations of M87*. In conformal gravity, large values of $m_2$ and $Q_s$ must be excluded. In STEGR $f(Q)$ gravity the observational limits on the parameter $\alpha$ are: $-0.025<\alpha<0.04$. For an alternative generalization of the Bumblebee model with the Schwarzschild approximation: $-0.3 < l < 0.45$. These results demonstrate the maximum one can achieve without taking into account of the rotation of a black hole.

Gauss–Bonnet holographic superconductors in lower dimensions

We disclose the effects of Gauss–Bonnet gravity on the properties of holographic s-wave and p-wave superconductors, with higher-order corrections, in lower-dimensional spacetime. We employ shooting method to solve equations of motion numerically and obtain the effect of different values of mass, nonlinear gauge field and Gauss–Bonnet parameters on the critical temperature and condensation. Based on our results, increasing each of these three parameters leads to lower temperatures and larger values of condensation. This phenomenon is rooted in the fact that conductor/superconductor phase transition faces with difficulty for higher effects of nonlinear and Gauss–Bonnet terms in the presence of a massive field. In addition, we study the electrical conductivity in holographic setup. In four dimension, real and imaginary parts of conductivity in holographic s- and p-wave models behave similarly and follow the same trend as higher dimensions by showing the delta function and divergence behavior at low-frequency regime that Kramers–Kronig relation can connect these two parts of conductivity to each other. We observe the appearance of a gap energy at $$\omega _{\mathrm{g}}\approx 8T_{\mathrm{c}}$$ which shifts toward higher frequencies by diminishing temperature and increasing the effect of nonlinear and Gauss–Bonnet terms. Conductivity in three dimensions is far different from other dimensions. Even the real and imaginary parts in s- and p-wave modes pursue various trends. For example in $$\omega \rightarrow 0$$ limit, imaginary part in holographic s-wave model tends to infinity but in p-wave model approaches to zero. However, the real parts in both models show a delta function behavior. In general, real and imaginary parts of conductivity in all cases that we study tend to a constant value in $$\omega \rightarrow \infty $$ regime.

On charged black holes in 4D Lovelock theory coupled to ModMax nonlinear electrodynamics

The ModMax nonlinear electrodynamics is a recently proposed model which possesses maximally symmetries among the well-known nonlinear electrodynamics models. This model consists of both Maxwell’s invariants such that in the absence of either the electric or the magnetic field the model automatically reduces to the Maxwell linear theory. The presence of both scalar invariants which are necessary for the symmetries of the model makes it very special such that cannot be employed in higher or lower dimensions. Unfortunately, we observed in the literature that, this model has been applied in higher d-dimensions. This is still an early time for this model, however, it is becoming popular. We aim to clarify this specific important point by giving the correct approach to the 4D Einstein–Gauss–Bonnet gravity as well as 4D Einstein p-order Lovelock theory coupled to ModMax nonlinear electrodynamics.

Are parametrized tests of general relativity with gravitational waves robust to unknown higher post-Newtonian order effects?

Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general relativity (a realization of the parametrized post-Einsteinian framework), where the gravitational waveform, as calculated in Einstein's theory as a series expansion in the orbital velocity, is parametrically deformed at a given set of orders in velocity. However, most current approaches usually only analyze the data while considering a single, specific modification at a time. Are then constraints placed with a single modification robust to our ignorance of higher post-Newtonian order corrections? We show here that for a wide class of theories, specifically those that admit a post-Newtonian expansion, single-parameter tests are indeed robust. In particular, through a series of full Bayesian parameter estimation studies on several different sets of synthetic data, we show that single-parameter constraints are not degraded but rather are improved by the inclusion of multiple parameters, provided one includes information about the mathematical structure of the series. We then exemplify this with a specific theory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where the waveform has been calculated to higher post-Newtonian orders than leading. We show that the inclusion of these higher order terms strengthens single-parameter constraints, instead of weakening them, and that the strengthening is very mild. This analysis therefore provides strong evidence that single-parameter post-Einsteinian tests of general relativity are robust to ignorance of high post-Newtonian order terms in the general relativistic deformations.

Gravitational Analysis of Rotating Charged Black‐Hole‐Like Solution in Einstein–Gauss–Bonnet Gravity

AbstractThis work analyzes the Einstein–Gauss–Bonnet gravity of charged black hole solutions through Newman–Janis approach. The Hawking temperature for corresponding black hole is also computed. The solution depends upon rotation parameter a, black hole mass, charge and horizon. Moreover, the graphical behavior of temperature via event horizon to analyze the stability of black hole under the effects of rotation parameter is discussed. The graphs are plotted in the presence/absence of rotation parameter and charge. Furthermore, the Hawking temperature under gravity effects is studied by using the semi‐classical method. It is also observed that the maximum temperature at non‐zero horizon depicts the BH remnant. Finally, the logarithmic corrected entropy for given black hole is computed and the logarithmic corrected entropy under effects of rotation and correction parameter are studied.

Anisotropic compact stars in presence of electromagnetic field, quintessence field and cosmological constant in f(G) gravity

In this work, we have discussed the anisotropic compact stars in the framework of modified Gauss–Bonnet gravity, named by f(G) theory of gravity. We have found the equations of motion of stars with respect to spherically symmetric metric, describing interior geometry of the compact stellar object, anisotropic mode of the matter distribution in the presence of electromagnetic field and quintessence field. We have taken the metric coefficients in the form [Formula: see text] and [Formula: see text] as well as a particular form of [Formula: see text], where the powers and coefficients of r are constants. The unknown constants are evaluated by matching between interior and exterior Reissner–Nordström–de Sitter metric. We have analyzed some physical aspects like energy density, radial and tangential pressures, anisotropic parameter of matter distribution, energy conditions, mass-radius relation, compactness factor, surface redshift, and stability of our resulting solutions through graphical behavior by comparing to the observational data of different types of compact stars like 4U1820-30, Vela X-1 and SAXJ1808.4-3658. We conclude that all physical attributes maintain their experimental ranges which deliver our anisotropic compact star models are viable and also stable upto certain region in [Formula: see text] gravity theory.

Anisotropic compact objects with Finch–Skea geometry in EGB gravity

We present a new class of relativistic anisotropic stellar models with spherically symmetric matter distribution in Einstein Gauss–Bonnet (EGB) gravity. A higher dimensional Finch–Skea geometry in the theory is taken up here to construct stellar models in hydrostatic equilibrium. The Gauss–Bonnet term is playing an important role in accommodating neutron stars. We study the physical features namely, the energy density, the radial and tangential pressures and the suitability of the models. It is found that the equation of state of such stars are non-linear which is determined for a given mass and radius of known stars. The stability of the stellar models are also explored for a wide range of values of the model parameters.

Minimally deformed charged stellar model by gravitational decoupling in 5D Einstein–Gauss–Bonnet gravity

We investigate the possibility of existing a class of compact charged spheres made of a charged perfect fluid in the framework of Einstein–Gauss–Bonnet theory in five-dimensional spacetime (5D EGB). In order to study spherically symmetric compact stars in EGB gravity, we prefer to apply a systematic and direct approach to decoupling gravitational sources via the minimal geometric deformation approach (MGD), which allows us to prove that the fluid must be anisotropic. In fact, we specify a well-known Krori–Barua spacetime in the MGD approach that helps us to determine the decoupling sector completely. Indeed, by using this approach, we found an exact and physically acceptable solution which satisfies all the elementary criteria of physical acceptability for a stellar solution via mimic approach. Finally, we show that the compactness factor in the presence of gravitational decoupling satisfies the Buchdahal limit under 5D EGB gravity.

Holographic superconductivity in Einsteinian Cubic Gravity

We study the condensation of a charged scalar field in a (3 + 1)-dimensional asymptotically AdS background in the context of Einsteinian cubic gravity, featuring a holographic superconductor with higher curvature corrections corresponding to a CFT with a non-vanishing value of the stress tensor three-point function t4. As it was previously noticed for higher dimensional Gauss-Bonnet theory, we observe that the critical temperature of the superconducting phase transition is lowered as the higher curvature coupling grows.

Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.