Extended Tolman–Oppenheimer–Volkoff Equation in f(R,A) gravity

Abstract

This paper provides a more general version of the Tolman–Oppenheimer–Volkoff equation that shows the hydrostatic equilibrium in the context of the gravitational theory $f(R,A)$. This theory is one of several modified theories of gravity that have been proposed. Anisotropic matter content is considered to investigate the compact objects’ equilibrium structure. This work is focused on the linear model $R+\alpha A$, in which $R$ is the Ricci scalar, $A$ is the anticurvature scalar, and $\alpha$ is the coupling factor. To solve the modified Tolman–Oppenheimer–Volkoff equation, we obtained suitable metric potential functions using the Karmarkar condition and employing an appropriate equation of state. We also determine an extended mass function by using the field equations. In this work, we have found a numerical solution of the dimensionless Tolman–Oppenheimer–Volkoff equation and plotted the mass–radius relation alongside several physical quantities, including radial pressure, mass function, scalar curvature, anisotropy, and the force acting on the system. We conduct the entire analysis using three compact stars: Cen X-3, Her X-1, and LMC X-4. Due to the complexity of the Tolman–Oppenheimer–Volkoff equations, we have employed the numerical technique to find various unknowns that appeared in the problem.