Stability of regular energy density in Palatini $$f(R)$$ f ( R ) gravity

The present work explores the effects of the three-parametric $$f(R)$$ model on the stability of the regular energy density of planar fluid configurations with the Palatini $$f(R)$$ formalism. For this purpose, we develop a link between the Weyl scalar and structural properties of the system by evaluating a couple of differential equations. We also see the effects of Palatini $$f(R)$$ terms in the formulation of structure scalars obtained by orthogonal splitting of the Riemann tensor in general relativity. We then identify the parameters which produce energy density irregularities in expansive and expansion-free dissipative as well as non-dissipative matter distributions. It is found that particular combinations of the matter variables lead to irregularities in an initially homogeneous fluid distribution. We conclude that Palatini $$f(R)$$ extra corrections tend to decrease the inhomogeneity, thereby imparting stability to the self-gravitating system.