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It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein-Gauss-Bonnet (EGB) gravity. This motivates the questions: in EGB does the conformal flatness criterion yield the Schwarzschild metric? Does the assumption of constant density gen...

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... For a study of the physical features in stellar models it is necessary to find exact solutions to the EGB field equations. Particular classes of exact solutions in static metrics have been found mainly in five and six spacetime dimensions [30][31][32][33][34][35] for neutral matter distributions with isotropic pressure. Other interesting models have been studied by [36][37][38][39]. ...

We generate the Einstein–Gauss–Bonnet field equations in higher dimensions for a spherically symmetric static spacetime. The matter distribution is a neutral fluid with isotropic pressure. The condition of isotropic pressure, an Abel differential equation of the second kind, is transformed to a first order nonlinear canonical differential equation. This provides a mechanism to generate exact solutions systematically in higher dimensions. Our solution generating algorithm is a different approach from those considered earlier. We show that a specific choice of one potential leads to a new solution for the second potential for all spacetime dimensions. Several other families of exact solutions to the condition of pressure isotropy are found for all spacetime dimensions. Earlier results are regained from our treatments. The difference with general relativity is highlighted in our study.

... Moreover, some models related to compact objects have been studied in Refs. [27][28][29][30][31]. ...

Within the framework of Einstein-Gauss-Bonnet theory in five-dimensional spacetime ($5D$ EGB), we derive the hydrostatic equilibrium equations and solve them numerically to obtain the neutron stars for both isotropic and anisotropic distribution of matter. The mass-radius relations are obtained for SLy equation of state, which describes both the solid crust and the liquid core of neutron stars, and for a wide range of the Gauss-Bonnet coupling parameter $\alpha$. More specifically, we find that the contribution of the Gauss-Bonnet term leads to substantial deviations from the Einstein gravity. We also discuss that after a certain value of $\alpha$, the theory admits higher maximum masses compared with general relativity, however, the causality condition is violated in the high-mass region. Finally, our results are compared with the recent observations data on mass-radius diagram.

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 (5 D 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.

We study the influence of higher curvature effects on stellar structure and conclude that the properties of stars are greatly impacted when such terms are dynamic. In particular, the surface gravitational redshift, which is connected to the equation of state and also the mass-radius ratio, differs greatly from the corresponding values in general relativity as evidenced through our empirical comparisons. A model of a superdense star with strange star equation of state is constructed within the framework of the Einstein-Gauss-Bonnet theory. Under these assumptions large classes of solutions are admitted by the field equations. We isolate a particular class with the ansatz of the Vaidya-Tikekar superdense star spatial gravitational potential. The model is found to satisfy elementary requirements for physical applicability and stability. The parameter values chosen are consistent with observed star models. A significant effect of the higher curvature terms is to reduce the speed of sound and to drastically reduce the values of the surface gravitational redshift compared to the Einstein counterpart. These latter results have implications for interpretations of observations in relativistic astrophysics which are often made against the background of the standard general theory of relativity. Additionally, our results suggest a value for the Gauss-Bonnet coupling of the order of 103 in the context of strange stars.

In this work we explore the characteristics of a polytropic solution for the anisotropic stellar object within the framework of Einstein–Gauss–Bonnet (EGB) gravity.We introduce anisotropy via the minimally gravitational decoupling method. The analysis of the exact solution of the governing equation for the gravitational potentials reveals novel features of the compact object.We find that the EGB-coupling constant and the decoupling parameter play important roles in enhancing and suppressing the effective density and radial
profiles at each interior point of the bounded object.An analysis of the effective tangential pressure reveals a ‘changeover’ in the trends brought about by the EGB and decoupling constants which may be linked to the cracking observed in classical 4D stellar objects proposed by Herrera (Phys Lett A 165:206, 1992).

The static isotropic gravitational field equation, governing the geometry and dynamics of stellar structure, is considered in Einstein–Gauss–Bonnet (EGB) gravity. This is a nonlinear Abelian differential equation which generalizes the simpler general relativistic pressure isotropy condition. A gravitational potential decomposition is postulated in order to generate new exact solutions from known solutions. The conditions for a successful integration are examined. Remarkably we generate a new exact solution to the Abelian equation from the well known Schwarzschild interior seed metric. The metric potentials are given in terms of elementary functions. A physical analysis of the model is performed in five and six spacetime dimensions. It is shown that the six-dimensional case is physically more reasonable and is consistent with the conditions restricting the physics of realistic stars.

In this endeavour, we model spherically, symmetric compact stellar configurations obeying a polytropic equation of state of the form pr=κρ2+βρ-γ within the framework of Einstein–Gauss–Bonnet gravity. We employ the Finch and Skea ansatz to complete the gravitational behaviour of the stellar fluid. The solution is smoothly matched to the exterior Boulware–Deser metric. The effect of the EGB coupling constant is highlighted by studying the thermodynamical properties and stability of the stellar model.

We present an exact solution that could describe compact star composed of color-
flavor locked (CFL) phase. Einstein's �eld equations were solved through CFL equation of
state (EoS) along with a speci�c form of grr metric potential. Further, to explore a
generalized solution we have also included pressure anisotropy. The solution is then
analyzed by varying the color superconducting gap � and its e�ects on the physical
parameters. The stability of the solution through various criteria is also analyzed. To
show the physical validity of the obtained solution we have generated the M-R curve
and �fitted three well-known compact stars. This work shows that the anisotropy of the
pressure at the interior increases with the color superconducting gap leading to decrease
in adiabatic index closer to the critical limit. Further, the fluctuating range of mass due to the density perturbation is larger for lower color superconducting gap leading to more stable configuration.

In this paper we present two new classes of solutions describing compact objects within the framework of five‐dimensional Einstein‐Gauss‐Bonnet (EGB) gravity. We employ the Complete Geometric Deformation (CGD) formalism which extends the Minimal Geometric Deformation (MGD) technique adopted in earlier investigations to generate anisotropic models from known isotropic solutions. The two solutions presented arise from mimicking the constraint for the pressure and density respectively which generate independent deformation functions. Rigorous physical tests show that contributions from CDG suppress the effective pressure but enhances the effective density and mass of the compact object, with the suppression/enhancement being modified by the EGB coupling constant. One of the highlights in our findings is that the deformation function along the radial component in CDG is nonzero at the boundary when we mimic both the pressure and density while in MGD we observe a vanishing of this deformation function at the boundary of the fluid configuration only for the pressure constraint. The difference in behavior of the deformation function at the surface predicts different stellar characteristics such as mass‐to‐radius and surface redshifts.