Comparative geometric approaches to electrically charged anisotropic compact stars within the Einstein–Maxwell framework

In this paper, we investigate three distinct approaches — physical, geometric, and curvature based — which may be regarded as specific restrictions imposed on the spacetime manifold. These assumptions are motivated by the expectation that realistic compact stellar configurations may exhibit such structural, geometric, and curvature characteristics. Under these considerations, we construct static, spherically symmetric, charged, anisotropic compact star models within the Einstein–Maxwell framework. The vanishing complexity condition regulates the interplay between density inhomogeneity and pressure anisotropy, thereby simplifying the matter distribution. The embedding class-one condition imposes geometric constraints on the metric via higher-dimensional embeddings, effectively reducing the degrees of freedom in the field equations. Conformal flatness enforces the vanishing of the Weyl tensor, constraining spacetime curvature and ensuring local conformal symmetry. Each approach reduces the two-metric potential problem to a single generating function through appropriate bridging relations, with suitable assumptions on the charge distribution maintaining consistency with the Einstein–Maxwell system. We discuss solution strategies, matching conditions at the exterior Reissner–Nordström spacetime, and physical viability criteria. A comparative assessment of the advantages, limitations, and characteristic observable predictions of each approach is provided, emphasizing their synergistic role in deriving exact, physically consistent stellar models.