Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit $$2M/R \le 8/9$$ 2 M / R ≤ 8 / 9 . Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated 3-space.

In recent years, there has been a growing interest in stellar modeling in the framework of Einstein–Gauss–Bonnet gravity. In this paper, for a relativistic star in static equilibrium, we invoke the five-dimensional Einstein–Gauss–Bonnet gravity and solve the system by assuming a matter distribution that admits a linear equation of state. We fix the model parameters by matching the interior solution to the exterior Boulware–Deser metric, which facilitates physical analysis of the resultant configuration. We analyze the star’s gross physical properties, which brings to attention the role of the Gauss–Bonnet coupling parameter [Formula: see text] in fine-tuning the values of the matter variables.

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