Anisotropic stellar compact spheres in f(R) gravity via Karmarkar approach

This paper investigates the new interior solution of stellar compact spheres in the framework of metric f(R) gravity. In this connection, we derived the Einstein field equations for static anisotropic spherically symmetric spacetime in the mechanism of Karmakar condition. The obtained results of the field equations have been studied with well-known Starobinskian model f(R) = R + zeta R-2 by using three different compact stars like RXJ1856-37, HerX-1, VelaX-12. Moreover, the constants involved in the solution of metric potentials have been determined through smooth matching conditions between the interior geometry and exterior spacetime. Thereafter, the physical significance of the obtained results is examined in the form of fluid variables, equation of state (EoS) parameters, energy conditions, anisotropic stress and stability analysis by using the graphical plot. The approximated values of the constants and the mass-radius relation have been calculated through different stellar star objects (RXJ1856-37 (rb = 6Km), HerX-1 (r(b) = 6.7Km) and VelaX-12 (r(b) = 9.99Km)) shown in Table 1. Finally, we have concluded that our considered compact stellar objects with particular choice of f(R) model in the mechanism of Karmakar condition satisfies all the necessary bounds for potentially stable formation of the stars.