Impact of Equation of State Parameters on the Complexity of Anisotropic Stellar Models

In this work, we investigate the role of equation of state (EOS) parameters in governing the complexity of static, self-gravitating stellar systems. Employing Herrera’s definition of complexity for static, spherically symmetric configurations within the framework of general relativity [L. Herrera, Phys. Rev. D 97, 044010 (2018)], we study three anisotropic stellar models constructed using the Vaidya–Tikekar background geometry together with different equations of state. The complexity factor provides a useful tool for probing the internal structure of self-gravitating astrophysical objects. For static, spherically symmetric fluid distributions with anisotropic pressure, complexity is fundamentally associated with energy density inhomogeneity and the anisotropic distribution of stresses. The complexity factor, defined through the orthogonal splitting of the Riemann tensor, quantifies the interplay between pressure anisotropy and density inhomogeneity within the system.

The Vaidya–Tikekar metric is an important exact solution of Einstein’s field equations that is widely used in relativistic astrophysics to model compact stellar objects such as neutron stars and strange stars. In this model, the interior spacetime of a static, spherically symmetric star is assumed to be pseudo-spheroidal rather than perfectly spherical. The Vaidya–Tikekar metric, previously shown to effectively describe compact and dense stellar objects, is adopted as the underlying spacetime geometry.

In this model, we perform a systematic analysis of the impact of EOS parameters on the complexity factor and its individual contributions. Our results demonstrate a strong dependence of the complexity factor on the EOS parameters. In particular, we observe that the complexity of anisotropic stellar configurations increases monotonically with increasing EOS parameters for all equations of state considered. Using current observational data of the pulsar 4U-1608, we show the impact of the EOS parameter in our model, supported by graphical depictions. These findings underscore the crucial influence of the equation of state on the structural complexity and internal organization of relativistic compact stars.