Impact of the tangential velocity and Karmarkar condition in constructing wormhole solutions within Rastall-Rainbow gravity

Abstract

In this paper, we analyze the existence of asymptotically flat wormhole solutions in the realm of Rastall-Rainbow modified gravity through an approach that combines aspects of Rastall gravity with the Rainbow framework. Using the Karmarkar condition for embedding class one metrics, we analytically solve the modified field equations that characterize wormholes. We examine the feasibility of our proposed shape functions through a graphical analysis. Interestingly, we used the rotational velocity formula to calculate the redshift function. We also examined the energy conditions to analyze the physical content of the wormhole and determined that the exact wormhole models are composed of exotic matter. This exotic matter violates the necessary energy conditions near the wormhole throat, ensuring that the wormholes remain traversable and consistent with their theoretical framework. Our findings also demonstrated the positive deflection angle for photons following null geodesics.