Gauss-Bonnet Parameter Research Articles

Exploring perfect fluid dark matter with EHT results of Sgr A* through rotating 4D-EGB black holes

We investigate the rotating 4D Gauss–Bonnet (GB) black holes surrounded by Perfect Fluid Dark Matter (PFDM) using the Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A*). This rotating black hole, influenced by an additional GB parameter α and a DM parameter β, deviates from the Kerr black hole geometry, offering a more complex horizon structure. Our findings reveal that the shadow size decreases and oblateness increases with higher values of α, β, and the spin parameter a. By plotting the shadow area A and oblateness D as functions of α and β for various a values, we determine the unique black hole parameters through the intersection points of the A and D curves. We constrain the GB and DM parameters with the EHT shadow observational results of Sgr A* for an inclination angle of 90° and 50°. The results, which align with EHT observations of Sgr A*, suggest that dark matter may exist in significant quantities around the galactic centre, challenging the traditional Kerr black hole model and offering new avenues for understanding complex interactions. Thus, It is essential to consider that rotating 4D GB black holes surrounded by PFDM could be strong candidates for astrophysical black holes.

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.

Particle acceleration near a rotating charged black hole in 4D Einstein-Gauss-Bonnet gravity

We investigate the horizon structure and ergosphere in a charged rotating black hole within 4D Einstein-Gauss-Bonnet gravity, which introduces additional parameters (Q) because of the charge and Gauss-Bonnet parameter (β), besides the mass (M) and rotation parameter (a). Interestingly, for each value of the parameter Q (β), there is a critical GB parameter β=βE (Q=QE) that corresponds to an extremal black hole with degenerate horizons. For β<βE (Q<QE), it describes a non-extremal black hole with two horizons, and for β>βE (Q>QE), no black hole exists. The extremal value βE (QE) is also affected by the GB parameter α and the ergosphere. We also study the collision of two equal-mass particles near the horizon of this black hole and explicitly show the effect of the parameter β (Q). The innermost stable circular orbits (ISCO) and the effective potential, which governs the motion of particles in spacetime, have been analyzed for different parameter values. The centre-of-mass energy (ECM) depends on the rotation parameter a and the parameters β and Q. We investigate the ECM of two colliding particles near the horizon for both extremal and non-extremal cases. It is shown that in extremal cases, when one of the colliding particles has a critical angular momentum, the ECM can be arbitrarily high, suggesting that the charged rotating in 4D Einstein-Gauss-Bonnet gravity can function as a particle accelerator. Despite the complexity of the BH solution, an exact expression for the thermodynamic quantities of black holes, such as the mass, Hawking temperature, and entropy, is derived in terms of the horizon radius. These quantities show significant deviations from the Kerr solution because of the influence of the Gauss-Bonnet parameter and electric charge.

Tidal effects in 4D-charged Einstein-Gauss-Bonnet gravity black hole

In this paper, we study the geodesic deviation between two nearby geodesics. For this process, we calculated the geodesic equation and radial motion of test particles. Also, the radial and angular tidal forces have been investigated using the curvature tensor in tetrad form. The radial tidal forces in 4D charged Einstein-Gauss-Bonnet gravity black hole show a tidal effect with a small value of radial coordinate r. The angular tidal forces show converse behavior as compared to the radial tidal forces at the short value of radial coordinate r. The radial and angular tidal forces have the same behavior at the immense value of radial coordinate r. The geodesic deviation paths depend on the charge Q parameter and Gauss-Bonnet parameter α of the black hole. We have compared our result with the 4D uncharged Einstein-Gauss-Bonnet gravity black hole and Reissner-Nordström with consideration of two kinds of initial conditions.

Holographic Einstein rings of a Gauss–Bonnet AdS black hole

Based on the AdS/CFT correspondence, we study the holographic Einstein image of a Gauss–Bonnet AdS black hole in the framework of wave optics. Our results show that for the absolute amplitude of total response function, there always exists the interference pattern when the scalar wave passes through black hole. And, the value of the amplitude depends closely on the properties of Gaussian source and spacetime geometry. More importantly, we also find that the holographic images always appears as a ring surrounded by the concentric stripe when observer located at the north pole. At other positions, this ring will change into a luminosity-deformed ring, or two light points. In addition, the influence of Gauss–Bonnet parameter alpha , wave source and optical system on the holographic image have been carefully addressed and the results show that the radius of ring is dependent of the Gauss–Bonnet parameter alpha but not dependent of wave source and optical system. The holographic images that different types of black holes have different features may shed deep insights on the existence of a gravity dual for a given material.

4D Einstein-Gauss-Bonnet black hole in Power-Yang-Mills field: a shadow study

We consider a static black hole immersed in the Power-Yang-Mills field in four-dimensional Einstein-Gauss-Bonnet gravity and investigate the effect of various parameters on the radius of the photon sphere. The modified form of the Newman-Janis algorithm is used for obtaining a rotating black hole solution in this gravity. Further, we try to explore the influence of the Yang-Mills magnetic charge Q with power q, Gauss-Bonnet parameter α, and spin a on the horizon radius. The geodesic equations are constructed by incorporating the Hamilton-Jacobi formalism. The radial component of the geodesic equations gives the effective potential which is further used in deriving the mathematical structure for the shadows by using Bardeen's procedure for a fixed observer at infinity. The shadows are calculated and plotted in terms of two celestial coordinates for an equatorial observer. It is observed that all the parameters have a very significant effect on the shadow and related physical observables. We also obtain the constraint values for the spin, magnetic charge, and Gauss-Bonnet parameters, using the shadow size of supermassive black holes Sagittarius A* and M87* from the EHT observations for the cases of q = 0.6 and q = 0.9. It is shown that there are upper and lower bounds for the charge and spin of M87* at q = 0.6, while only the upper bounds for the charge and spin of Sagittarius A*. Finally, we investigate the energy emission rate in the Hawking radiation around the 4D Einstein-Gauss-Bonnet black hole in the Power-Yang-Mills field.

4D-EGB black holes in RPS thermodynamics

In this paper, we study thermodynamics of charged and uncharged 4-Dimension Einstein-Gauss–Bonnet (4D-EGB) black holes. The context of this study is the Visser’s holographic thermodynamics with a fixed anti-de Sitter radius and a variable Newton constant known as restricted phase space thermodynamics (RPST). Our setup is constructed by using the AdS/CFT correspondence and by introducing a conjugate quantity of the Gauss–Bonnet parameter. By this ansatz, we conclude that the Gauss–Bonnet action multiplied by a temperature, behaves as a free energy. We derive the conjugate quantities corresponding to the first law in the RPST formalism. The study of the T−S processes and the effect of the Gauss–Bonnet constant, α, show that thermodynamic properties of charged black holes depend on the Gauss–Bonnet term and the charge of black holes. For an uncharged black holes, the effect of Gauss–Bonnet becomes crucial, as it behaves as a charged black hole with an effective charge. Finally, we find that the Hawking-Page phase transition occurs between a large black hole and a thermal AdS space.

Rotating black hole in 4D Einstein–Gauss–Bonnet massive gravity: Shadow and center of mass energy

This work comprises the derivation of a rotating black hole metric by applying the modified Newman-Janis algorithm to a static four dimensional black hole in Einstein-Gauss–Bonnet massive gravity. We choose several parametric values to study the influence of graviton mass m and the Gauss–Bonnet parameter α on the horizon radii and photon sphere’s radii of the rotating and non-rotating black holes, respectively. By considering the Hamilton–Jacobi method, we construct the geodesic equations and by using Bardeen’s procedure of impact parameters, we study the effect of graviton mass on the effective potential, shadow, distortion and energy emission rate. We find that the graviton mass has a very significant effect on the shadow and related physical observables. In the vicinity of the black hole, we investigate the collision of two uncharged particles. We compute the energy of the particles in the center of mass frame for the static and rotating BH cases. Finally, the shadow diameter is compared with Sgr. A* to obtain the constraints on the black hole parameters.

Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity

This work provides the exact solution of the Bardeen black hole in association with [Formula: see text] Gauss–Bonnet massive gravity in Anti-de-Sitter [Formula: see text] space–time. It is a modification of the Gauss–Bonnet when gravity couples with nonlinear matter fields which is the function of the electromagnetic field. The obtained solution gives rise to [Formula: see text] EGB Bardeen black holes when the massive gravity parameter is set to zero and it yields a [Formula: see text] Gauss–Bonnet black hole in the absence of magnetic monopole charge. Further, we analyze and adopt the thermodynamic quantities like mass ([Formula: see text]), temperature [Formula: see text] and heat capacity [Formula: see text] in the presence of massive gravity and nonlinear electrodynamics. In addition, we extend our results by considering the cosmological constant [Formula: see text] as a thermodynamical variable [Formula: see text] and obtain the critical values of pressure, temperature, horizon radius and analyze the behavior of the global parameter [Formula: see text]. The effect of a massive parameter ([Formula: see text]) of the critical exponent is opposite to the magnetic monopole charge ([Formula: see text]) and Gauss–Bonnet parameter ([Formula: see text]). According to our analysis the phase transition between a small and large black hole and van der Waals phase transition are analogous to each other.

Breaking of the universal nature of the central charge criticality in AdS black holes in Gauss-Bonnet gravity

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($\Lambda$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\alpha$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this universal nature breaks when such phase transition is considered for black holes in the Gauss-Bonnet gravity. Apart from this, treating the Gauss-Bonnet parameter as a thermodynamic variable as suggested in \cite{kastori} in light of the consistency between first law and the Smarr relation leads to modified thermodynamic volume (conjugate to variable cosmological constant), adding to a new understanding of the Van der Waals gas like behaviour of the black holes in higher dimensional and higher curvature gravity theories. Our analysis considers a general $D$ dimensional background. We have then imposed a greater focus in the analysis of the phase structure of the five dimensional Gauss-Bonnet spacetime. Our analysis also shows that the general universal nature of the critical value of the central charge (which was present in four dimensional $AdS$ spacetime), breaks down in case of five dimensional $AdS$ spacetime even in the absence of Gauss-Bonnet gravity. This finding indicates the universal nature of the central charge may be a special feature of the four dimensional $AdS$ spacetime only.

Cluster of stars in f(, T) gravity

This paper is devoted to analyze the dynamical impacts of gravity model on the cluster of stars. For this motive, we consider the spherically symmetric interior geometry with anisotropic fluid as analogous to cluster of stars distributions. We express the modified field equations by taking a particular model of , i.e. . In order to explore the evolutionary behavior of cluster of stars, the observational data of a compact star 4U1820 − 30 is used. We construct the modified scalar functions by orthogonal splitting of Riemann tensor in theory of gravity and find the factors causing density irregularities in the framework. We calculate the evolution parameters by using these scalar functions. Moreover, we also investigate the structure scalars for dust ball. The dynamical effects on cluster of stars are examined via structure scalars in the presence of Gauss-Bonnet gravity. It is found that Gauss-Bonnet parameter representing exotic material in the cluster plays a vital role in governing the dynamics of cluster of stars.

Magnetized and Magnetically Charged Particles Motion around Regular Bardeen Black Hole in 4D Einstein Gauss–Bonnet Gravity

In this paper, we study the horizon properties and scalar invariants of the spacetime around a regular black hole (BH) in 4D Einstein Gauss-Bonnet (4D EGB) gravity. It is observed that the presence of both Gauss-Bonnet (GB) coupling and magnetic charge parameters causes the shrinking of the outer horizon. We find that the range of the GB parameter α/M2∈(−0.15869,1), and the extreme value of magnetic charge reaches up to gextr=0.886M, which allows for the existence of a BH horizon, while it is gextr=0.7698M for pure Bardeen BH. We also investigate the dynamics of magnetized particles around the magnetically charged Bardeen BH, assuming the particle’s motion occurs in the equatorial plane in the proper observation frame, and the direction of the magnetic dipole moment of the particles is always kept radially and its magnitude is constant. Moreover, the dynamics of magnetically charged particles are also studied, and it is shown that both the energy and angular momentum of the particles corresponding to circular orbits increases with the increase of their magnetic charge. Finally, we also study collisions of magnetized, electrically neutral, and magnetically charged particles around the Bardeen BHs, where we provide analyses of critical angular momentum that may allow collision of the particles near-horizon radius, producing enormous values of center of mass energy of the collisions.

Polarized image of an equatorial emitting ring around a 4D Gauss–Bonnet black hole

We have studied the polarized image of an equatorial emitting ring around a 4D Gauss–Bonnet black hole. Our results show that the effects of Gauss–Bonnet parameter on the polarized image depend on the magnetic field configuration, the observation inclination angle, and the fluid velocity. As the magnetic field lies in the equatorial plane, the observed polarization intensity increases monotonously with Gauss–Bonnet parameter in the low inclination angle case, and its monotonicity disappears in the case with high inclination angle. However, as the magnetic field is vertical to the equatorial plane, the polarization intensity is a monotonously increasing function of Gauss–Bonnet parameter in the high inclination angle case. The changes of the electric vector position angle with Gauss–Bonnet parameter in both cases are more complicated. We also probe the effects of Gauss–Bonnet parameter on the Strokes Q–U loops.

Holographic consistency and the sign of the Gauss-Bonnet parameter

If Einstein-Gauss-Bonnet gravity is obtained as a low energy limit of string theory, then the Gauss-Bonnet parameter α is essentially the inverse string tension and thus necessarily positive. If one treats Einstein-Gauss-Bonnet gravity as a modified theory of gravity in the anti-de Sitter bulk in the bottom-up approach of holography, then there is no obvious restriction on the sign of the parameter a priori, though various studies involving boundary causality have restricted the possible range of α. In this short note, we argue that if holographic descriptions are to be consistent, then the Gauss-Bonnet parameter has to be positive. This follows from a geometric consistency condition in the Euclidean picture. From the Lorentzian signature perspective, black holes with a negative α lead to uncontrolled brane nucleation in the bulk and so the supposedly static geometry is untenable. In fact, even the ground state without a black hole is problematic. In other words, the bottom-up approach agrees with the top-down approach on the sign of the parameter. Some possible loopholes of the conclusion are discussed.

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.

Gravitational collapse involving electric charge in the decoupling limit of the dilatonic Gauss–Bonnet gravity

The paper discusses gravitational collapse of an electrically charged scalar field in the decoupling limit of the dilatonic Gauss–Bonnet gravity. The emerging spacetimes contained Schwarzschild black holes for sufficiently big scalar fields self-interaction strengths. Dependencies of the collapse characteristics on the dilatonic and Gauss–Bonnet parameters turned out to be similar in the case of black hole masses and radii as well as their time of formation in terms of retarded time. In the cases of masses and radii minima were observed, while in the remaining case a maximum existed. The electric charge of the emerging black holes possessed a maximum when measured versus the dilatonic coupling constant and was strictly decreasing with the Gauss–Bonnet coupling. The times of formation and charges of black holes decreased, while masses and radii increased with the self-interaction strengths of the dynamical fields. Values of the energy density, radial pressure, pressure anisotropy and the collapsing scalar fields were the biggest along the hypersurface of propagation of the scalar fields initial peaks. For big values of the Gauss–Bonnet coupling constant, an increase in their values was also observed in the vicinity of the central singularity within the whole range of advanced time. Non-zero values of the dilaton field outside the black hole event horizon may indicate a formation of a hairy black hole. The local temperature calculated along the apparent horizon was increasing for late times of the evolution and exhibited extrema in areas, where the dynamics of the gravity–matter system was observed.

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.

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.

Gravitationally Decoupled Strange Star Model beyond the Standard Maximum Mass Limit in Einstein–Gauss–Bonnet Gravity

Abstract The recent theoretical advance known as the minimal geometric deformation (MGD) method has initiated renewed interest in investigating higher-curvature gravitational effects in relativistic astrophysics. In this work, we model a strange star within the context of Einstein–Gauss–Bonnet gravity with the help of the MGD technique. Starting off with the Tolman metric ansatz, together with the MIT bag model equation of state applicable to hadronic matter, anisotropy is introduced via the superposition of the seed source and the decoupled energy-momentum tensor. The solution of the governing systems of equations bifurcates into two distinct models, namely, the mimicking of the θ sector to the seed radial pressure and energy density and a regular fluid model. Each of these models can be interpreted as self-gravitating static, compact objects with the exterior described by the vacuum Boulware–Deser solution. Utilizing observational data for three stellar candidates, namely PSR J1614–2230, PSR J1903+317, and LMC X-4, we subject our solutions to rigorous viability tests based on regularity and stability. We find that the Einstein–Gauss–Bonnet parameter and the decoupling constant compete against each other for ensuring physically realizable stellar structures. The novel feature of the work is the demonstration of stable compact objects with stellar masses in excess of M = 2 M ⊙ without appealing to exotic matter. The analysis contributes new insights and physical consequences concerning the development of ultracompact astrophysical entities.

Motion of particles and gravitational lensing around the (2+1)-dimensional BTZ black hole in Gauss\u2013Bonnet gravity

We study the motion of test particles and photons in the vicinity of the (2+1)-dimensional Gauss–Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, u_0, reaching a peak value for a specific u_0^*, and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.