Wormhole Solutions and Modified Tolman–Oppenheimer–Volkoff Equation

This article investigates wormhole geometry in modified f(R,ϕ,X) gravity, where R, ϕ, and X denote the Ricci scalar, scalar potential, and kinetic term, respectively. We also introduce charge to examine its influence on the wormhole geometry. In the present scenario, the Karmarkar condition is employed to determine the metric potentials. A key feature of this work is the derivation of the modified Tolman–Oppenheimer–Volkoff equation, which is used to analyze the stability of the wormhole geometry. We have analyzed the behavior of the matter-plus-charge energy conditions and found that the null energy condition is satisfied for the considered model, while the strong energy condition is violated. In contrast to general relativity, where the matter NEC must be violated to support a traversable wormhole, the present modified-gravity model fulfils the flare-out requirement through the effective energy–momentum tensor generated by the curvature–scalar–kinetic sector. Hence the required exoticity is shifted from ordinary matter to the effective modified-gravity sector. We also discuss the behavior of the equation-of-state parameters and anisotropy. Moreover, we perform an additional stability analysis based on the adiabatic index. Our analysis reveals that the wormhole solutions are stable for the considered model in modified f(R,ϕ,X) gravity.