Anisotropic model of stellar objects in modified f(R) gravity

Abstract

In this paper, we studied anisotropic models to describe compact stellar objects with a spherically symmetric matter distribution using modified $f\left(R\right)$ gravity. To accomplish this goal, we examined two distinct models within the $f\left(R\right)$ theory of gravity. We investigated the use of the Durgapal and Fuloria analog metric potentials to construct a stellar model by solving the Einstein Field equations. Our analysis includes a discussion of the generalized Darmois-Israel junction condition, crucial for smoothly linking the interior region to the Schwarzschild exterior metric at the star’s boundary hypersurface within the framework of $f\left(R\right)$ gravity. This junction condition requires a non-zero pressure at the boundary, which is directly related to the non-linear terms present in $f\left(R\right)$ gravity. These conditions are often overlooked by many researchers in their exploration of compact stellar models. In our study, we utilized generalized boundary conditions to determine model parameters. Furthermore, we obtained these parameters using observational data from several compact stars, including 4U1538-52, SAX J 1808.4-3658, EXO 1785-248, Cen X-3, 4U1820-30, PSR J1903+327, 4U1608-52, and PSR J1614-2230. This innovative approach allowed us to conduct a comprehensive analysis of models and their physical validity. We performed various physical tests such as anisotropy, equilibrium conditions, stability, energy-density constraints, mass function, compactness, redshift, and adiabatic index to evaluate the feasibility of our models.