Abstract
This work aims to identify some inhomogeneity factors for plane symmetric topology with anisotropic and dissipative fluid under the effects of both electromagnetic field as well as Palatini $f(R)$ gravity. We construct the modified field equations, kinematical quantities and mass function to continue our analysis. We have explored the dynamical quantities, conservation equations and modified Ellis equations with the help of a viable $f(R)$ model. Some particular cases are discussed with and without dissipation to investigate the corresponding inhomogeneity factors. For non-radiating scenario, we examine such factors with dust, isotropic and anisotropic matter in the presence of charge. For dissipative fluid, we investigate the inhomogeneity factor with charged dust cloud. We conclude that electromagnetic field increases the inhomogeneity in matter while the extra curvature terms make the system more homogeneous with the evolution of time.
Highlights
We found that the trace part of the second dual of the Riemann tensor has its dependence on the energy density profile of planar geometry with some extra curvature terms due to f (R) Palatini gravity while the remaining scalar functions have their dependence on the anisotropic stress tensor
We have investigated some inhomogeneity factors for a self-gravitating plane symmetric model
We have done this analysis by taking an anisotropic matter distribution in the presence of an electromagnetic field
Summary
Herrera et al [30,31] did a systematic study of the structure formation of self-gravitating compact stars by means of some scalar functions (trace and trace-free parts) obtained from splitting of the Riemann tensor These scalars are associated with electric and magnetic as well as second dual of the Riemann tensor and have an eventual relationship with the fundamental properties of the matter configuration [32]. While it is filled with a dissipative fluid by means of diffusion (heat) as well as free-streaming (null radiation) approximations having an anisotropic pressure in the interior Such matter fields are described by the energy-momentum tensor as follows: Tαβ = (P⊥ + μ)Vα Vβ + qβ Vα + εlαlβ + P⊥gαβ. The non-vanishing components of the electromagnetic stress tensor turn out to be
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