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# Variation of speed of sound with radius.

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