Abstract We investigate the stability of polytropic spheres in classical general relativity influenced by a departure from homogeneous spherical symmetry. We utilize the Vaidya–Tikekar ansatz to generate models of superdense stars obeying a polytropic equation of state of the form p r = κ ρ 1 + 1 n − β . Models with polytropic index n = 1 (quadratic equation of state) and n = 2 are generated for the general spheroidal parameter. We investigate the physical viability of these models and show that they describe strange star candidates such as SAX J1808.4-3658 to a good approximation. An interesting finding of this work shows that these models become unstable as the spheroidal parameter is decreased which leads us to conclude that stability is compromised with departure from homogeneous spherical symmetry.

中文翻译：

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球形度对多方球体稳定性的影响

摘要 我们研究了经典广义相对论中多方球体的稳定性受到偏离齐次球对称性的影响。我们利用 Vaidya-Tikekar ansatz 生成遵循 pr = κ ρ 1 + 1 n − β 形式的多方状态方程的超密度恒星模型。多方指数 n = 1（二次状态方程）和 n = 2 的模型是为一般球体参数生成的。我们研究了这些模型的物理可行性，并表明它们很好地近似描述了奇怪的候选恒星，例如 SAX J1808.4-3658。这项工作的一个有趣发现表明，随着球体参数的降低，这些模型变得不稳定，这使我们得出结论，稳定性会因偏离均匀球对称性而受到损害。