Gauss-Bonnet Research Articles

Applicability of modified Gauss–Bonnet gravity models on the existence of stellar structures

In this paper, we explore the existence of spherically symmetric strange quark configurations coupled with anisotropic fluid setup in the framework of modified Gauss–Bonnet theory. In this regard, we adopt two models such as (i)f(G)=βG2, and (ii)f(G)=δ1Gx(δ2Gy+1), and derive the field equations representing a static sphere. We then introduce bag constant in the gravitational equations through the use of MIT bag model, so that the quarks’ interior can be discussed. Further, we work out the modified equations under the use of Tolman IV ansatz to make their solution possible. Junction conditions are also employed to find the constants involved in the considered metric potentials. Afterwards, different values of model parameters and bag constant are taken into account to graphically exploring the resulting solutions. This analysis is done by considering five strange quark objects like Her X-I, LMC X-4, 4U 1820-30, PSR J 1614-2230, and Vela X-I. Certain tests are also applied on the developed models to check their physical feasibility. It is much interesting that this modified gravity under its both considered functional forms yield physically viable and stable results for certain parametric values.

Evolution of charged anisotropic spheres in Gauss–Bonnet gravity

Evolution of charged anisotropic spheres in Gauss–Bonnet gravity

An effective model for the quantum Schwarzschild black hole: Weak deflection angle, quasinormal modes and bounding of greybody factor

In this paper, we thoroughly explore two crucial aspects of a quantum Schwarzschild black solution within four-dimensional space–time: (i) the weak deflection angle, (ii) the rigorous greybody factor and, (iii) the Dirac quasinormal modes. Our investigation involves employing the Gauss–Bonnet theorem to precisely compute the deflection angle and establishing its correlation with the Einstein ring. Additionally, we derive the rigorous bounds for greybody factors through the utilization of general bounds for reflection and transmission coefficients in the context of Schrodinger-like one-dimensional potential scattering. We also compute the corresponding Dirac quasinormal modes using the WKB approximation. We reduce the Dirac equation to a Schrodinger-like differential equation and solve it with appropriate boundary conditions to obtain the quasinormal frequencies. To visually underscore the quantum effect, we present figures that illustrate the impact of varying the parameter r0, or more specifically, in terms of the parameter α. This comprehensive examination enhances our understanding of the quantum characteristics inherent in the Schwarzschild black solution, shedding light on both the deflection angle and greybody factors in a four-dimensional space–time framework.

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.

On a Reconstruction Procedure for Special Spherically Symmetric Metrics in the Scalar-Einstein–Gauss–Bonnet Model: the Schwarzschild Metric Test

On a Reconstruction Procedure for Special Spherically Symmetric Metrics in the Scalar-Einstein–Gauss–Bonnet Model: the Schwarzschild Metric Test

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Non‐isometric deformation in double curvature and symmetric composite laminates due to shrinkage

AbstractApplication of the global Gauss–Bonnet theorem for the prediction of changes in Gaussian curvature for double curvature laminate geometries due to shrinkage is developed for non‐isometric deformation states where in surface area change accompanies changes in curvature. The transition between isometric and non‐isometric deformation is strongly influenced by the ratio of the principal radii of curvature of the double curved surface and a relationship is proposed by the authors to accommodate the transition. Examples for the radii of curvature ratios of 2, 3, and 4 are compared to results from finite‐element simulations and the developed relationship is shown to be accurate within 0.55%. Furthermore, these results demonstrate that isometric deformation state can be taken as an adequate representation for double curvature toroidal laminate geometries of >10 and the class of materials studied in this work.Highlights Shrinkage induced deformation in multi‐curvature composite laminates is a recurring issue in polymer composite manufacturing. Thermal, crystallization and cure shrinkage are the dominant sources of shrinkage deformation in polymer composite systems. Isometric deformation of multi‐curvature, symmetric laminates composite is defined by the absence of membrane strain. The Gauss–Bonnet theorem provides a platform for determining radii of curvature changes in multi‐curvature symmetric laminates, Non‐isometric deformation of symmetric laminates can be treated by the Gauss–Bonnet theorem for radii of curvature ratios that correspond to geometric self‐constraint. The above highlights yield insight into the anticipated geometric distortions due to shrinkage in polymer composites.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Topology of black hole thermodynamics via Rényi statistics

In this paper, we investigate the topological numbers of the four-dimensional Schwarzschild black hole, d-dimensional Reissner–Nordström (RN) black hole, d-dimensional singly rotating Kerr black hole and five-dimensional Gauss–Bonnet black hole via the Rényi statistics. We find that the topological number calculated via the Rényi statistics is different from that obtained from the Gibbs–Boltzmann (GB) statistics. However, what is interesting is that the topological classifications of different black holes are consistent in both the Rényi and GB statistics: the four-dimensional RN black hole, four-dimensional and five-dimensional singly rotating Kerr black holes, five-dimensional charged and uncharged Gauss–Bonnet black holes belong to the same kind of topological class, and the four-dimensional Schwarzschild black hole and d(>5)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d(>5)$$\\end{document}-dimensional singly rotating Kerr black holes belong to another kind of topological class. In addition, our results suggest that the topological numbers calculated via the Rényi statistics in asymptotically flat spacetime background are equal to those calculated from the standard GB statistics in asymptotically AdS spacetime background, which provides more evidence for the connection between the nonextensivity of the Rényi parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} and the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}.

Weak Deflection Angle by the Einstein–Cartan Traversable Wormhole Using Gauss–Bonnet Theorem with Time Delay

Weak Deflection Angle by the Einstein–Cartan Traversable Wormhole Using Gauss–Bonnet Theorem with Time Delay

The Gauss–Bonnet theorem

The Gauss–Bonnet theorem is a crowning result of surface theory that gives a fundamental connection between geometry and topology. Roughly speaking, geometry refers to the “local” properties—lengths, angles, curvature— of some fixed object, while topology seeks to identify the “global” properties that are unchanged by a continuous deformation, such as stretching or twisting. The theorem formalizes an intuitive idea: continuous changes to curvature on one region of a surface will be balanced out elsewhere, so the total curvature of the surface stays the same. Explicitly, the Gauss–Bonnet theorem says that a surface’s total curvature, defined using its local Gaussian curvature, is directly proportional to the number of holes in the surface, which comes from an invariant quantity called its Euler characteristic. The Euler characteristic is a way of classifying which surfaces can be continuously deformed into one another; as an informal example, the classic joke that “a topologist is a person who cannot tell the difference between a coffee mug and a doughnut” comes from the fact that the objects each have one hole. Even though a coffee mug and a doughnut have visibly different geometric shapes, according to the Gauss–Bonnet theorem, both objects will have the same total curvature. The proof itself is delightfully systematic: we first find the total curvature of a curve on a plane, extend that result to curves on three-dimensional surfaces, extend that result to “polygons” on surfaces, and finally the entire surface. In Section 2, we prove Hopf’s Umlaufsatz for the total curvature of a simple closed curve in R2. Sections 3, 4, and 5 introduce concepts from differential geometry to define Gaussian curvature. In Section 6, we prove the local Gauss–Bonnet theorem for the total curvature of a surface polygon. At last, in Section 7, we prove the global Gauss–Bonnet theorem for compact surfaces by covering the surface with polygons and applying the local Gauss–Bonnet theorem to each one. Our discussion focuses on exposition, and references will be given in place of tedious computations when reasonable. This paper assumes a somewhat rigorous understanding of multivariable calculus and linear algebra, as well as some elementary group theory.

Reentrant Hawking–Page phase transition of charged Gauss–Bonnet-AdS black holes in the grand canonical ensemble

In this paper, we study the reentrant Hawking–Page transition in the grand canonical ensemble of Gauss–Bonnet AdS spacetime. We find that the four-dimensional Gauss–Bonnet hyperbolic AdS black hole always has a reentrant Hawking–Page transition in the range of electric potential 0<Φ<Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\Phi <\\Phi _{tr}$$\\end{document}, accompanied by the appearance of the triple point. However, once the potential exceeds a certain upper limit Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi _{tr}$$\\end{document}, i.e. Φ>Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi >\\Phi _{tr}$$\\end{document}, the Hawking–Page transition disappears. In the spacetime of five and higher dimensional Gauss–Bonnet hyperbolic AdS black hole, the reentrant Hawking–Page transition is solely observed to occur when the electric potential Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi $$\\end{document} lies between two specific thresholds (Φc<Φ<Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi _{c}<\\Phi <\\Phi _{tr}$$\\end{document}). In scenarios where the electric potential is below Φc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi _{c}$$\\end{document} (Φ<Φc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi <\\Phi _{c}$$\\end{document}), only the standard Hawking–Page transition as in the the Einstein gravity is observed. Similar to the four-dimensional case, the Hawking–Page transition is negated when the electric potential exceeds Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi _{tr}$$\\end{document} (Φ>Φtr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi >\\Phi _{tr}$$\\end{document}). We give the coexistence line, the triple point and critical point of the Hawking–Page transition in the phase diagram of the Gauss–Bonnet hyperbolic AdS black hole. The observed reentrant Hawking–Page transitions and triple points in the context of Gauss–Bonnet hyperbolic AdS black holes may correspond to the phase transitions and triple points in QCD phase diagrams, following the spirit of the AdS/CFT correspondence. To be a complete research, the Hawking–Page transition of d-dimensional charged spherical Gauss–Bonnet-AdS black hole in the grand canonical ensemble is also study in the Appendix, for which there exists a standard Hawking–Page transition with the transition temperature depending on the Gauss–Bonnet constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}.

General analysis of Noether symmetries in Horndeski gravity

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

Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives

Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives

The expansion behavior of the hyperbolic solution in f(R,G) gravity

In this study, our primary focus lies in meticulously exploring the intricacies of the universe by employing a flat Friedmann–Lemaître–Robertson–Walker (FLRW) model within the framework of [Formula: see text] gravity. In our analysis, the [Formula: see text] function is delineated as the sum of two distinct components, commencing with a quadratic correction of the geometric term denoted by [Formula: see text], structured as [Formula: see text], alongside a matter term denoted by [Formula: see text], where [Formula: see text] and [Formula: see text] symbolize the Ricci scalar and Gauss–Bonnet invariant, respectively. In the pursuit of solutions to the gravitational field equations within the [Formula: see text] formalism, we embrace a specific expression for the scale factor, represented as [Formula: see text] [D. Rabha and R. R. Baruah, The dynamics of a hyperbolic solution in [Formula: see text] gravity, Astron. Comput. 45 (2023) 100761]. In this context, the parameters [Formula: see text] and [Formula: see text] intricately shape the scale factor’s behavior. The model posits the intriguing prospect of perpetual cosmic acceleration when [Formula: see text], signifying a continuous expansion of the universe. Conversely, for [Formula: see text], the model proposes a pivotal transition from an early deceleration phase to the present accelerated epoch, a transformative shift in line with our understanding of cosmic evolution. Furthermore, the model demonstrates its credibility by satisfying Jean’s instability condition during the shift from a radiation-dominated era to a matter-dominated era, substantiating the formation of cosmic structures. In our analysis, a central focus is directed toward scrutinizing the equation of state parameter [Formula: see text] within our model. We delve into a comprehensive examination of the scalar field and meticulously assess the energy conditions surrounding the derived solution. To establish the robustness of our model, we deploy an array of diagnostic tools, including the Jerk, Snap, and Lerk parameters, along with the Om diagnostic, Classical stability of the model, and statefinder diagnostic tools, Observational Constraints on the Model Parameters. The outcomes, intertwined with a detailed analysis of both the results and the inherent intricacies of the model, are diligently clarified and presented.

Criticality of central charges for Gauss–Bonnet black holes

Employing extended phase space formalism, we study critical phenomenon of A-charge and C-charge for holographic theories dual to Gauss–Bonnet black holes. We find an universal critical Gauss–Bonnet coupling, giving rise to an universal ratio between the two central charges at the critical point. This leads to a new intepretation for critical behavior of Gauss–Bonnet black holes in terms of the boundary degrees of freedoms, although the solutions are electrically neutral. Another novel feature is for either of the central charges, the transition temperature is beyond the critical point but is upper bounded by causality of the boundary theories.

Unified first law of thermodynamics in Gauss–Bonnet gravity on an FLRW background

Unified first law of thermodynamics in Gauss–Bonnet gravity on an FLRW background

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

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

GUP corrected black holes with cloud of string

We investigate shadows, deflection angle, quasinormal modes (QNMs), and sparsity of Hawking radiation of the Schwarzschild string cloud black hole’s solution after applying quantum corrections required by the Generalised Uncertainty Principle (GUP). First, we explore the shadow’s behaviour in the presence of a string cloud using three alternative GUP frameworks: linear quadratic GUP (LQGUP), quadratic GUP (QGUP), and linear GUP. We then used the weak field limit approach to determine the effect of the string cloud and GUP parameters on the light deflection angle, with computation based on the Gauss–Bonnet theorem. Next, to compute the quasinormal modes of Schwarzschild string clouds incorporating quantum correction with GUP, we determine the effective potentials generated by perturbing scalar, electromagnetic and fermionic fields, using the sixth-order WKB approach in conjunction with the appropriate numerical analysis. Our investigation indicates that string and linear GUP parameters have distinct and different effects on QNMs. We find that the greybody factor increases due to the presence of string cloud while the linear GUP parameter shows the opposite. We then examine the radiation spectrum and sparsity in the GUP corrected black hole with the cloud of string framework, which provides additional information about the thermal radiation released by black holes. Finally, our inquiries reveal that the influence of the string parameter and the quadratic GUP parameter on various astrophysical observables is comparable, however the impact of the linear GUP parameter is opposite.