Modeling of self-gravitating compact configurations using radial metric deformation approach

Abstract

This study analyzes new analytical solution types that explore the influence of complexity on time-independent, spherically symmetric astrophysical configurations, based on a radial metric deformation scheme also known as minimal geometric deformation. We demonstrate that the complexity factor, a scalar function obtained via splitting the Riemann tensor orthogonally, exhibits an additive property. This implies that the overall complexity of a system containing two interacting fluid distributions (represented by Tμν and Φμν) is simply the sum of the individual complexities of each fluid. This work employs the radial metric deformation approach, a powerful tool for constructing astrophysically viable models of anisotropic matter, by building upon the Vaidya–Tikekar and Finch–Skea relativistic spacetimes. We observe that both the metric ansatzes produce qualitatively similar features, though the magnitudes may vary slightly, for any non-zero value of the decoupling parameter (0≤α<1). Interestingly, both models preserve their anisotropic nature despite reaching the zero-complexity limit (α=1). Finally,we delve into the physical implications of these novel solution types, examining their potential to accurately represent real compact configurations.