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.

中文翻译：

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探索 5D Einstein-Gauss-Bonnet Gravity 中引力解耦各向异性解的物理特性

在本文中，我们提出了两类新的解决方案，描述了五维爱因斯坦-高斯-博内 (EGB) 引力框架内的致密物体。我们采用完全几何变形 (CGD) 形式主义，它扩展了早期研究中采用的最小几何变形 (MGD) 技术，以从已知的各向同性解决方案生成各向异性模型。提出的两个解决方案分别来自模拟压力和密度的约束，它们生成独立的变形函数。严格的物理测试表明，CDG 的贡献抑制了有效压力，但提高了致密物体的有效密度和质量，抑制/增强由 EGB 耦合常数修改。我们发现的亮点之一是，当我们模拟压力和密度时，CDG 中沿径向分量的变形函数在边界处是非零的，而在 MGD 中，我们仅观察到该变形函数在流体配置的边界处消失为压力约束。表面变形函数行为的差异预示着不同的恒星特征，例如质量半径和表面红移。