Role of the complexity factor and Karmarkar condition in constructing new wormhole models in dRGT gravity

Abstract

This study delves into the distinctive characteristics of wormhole models in the context of de Rham-Gabadadze-Tolley (dRGT) massive gravity, providing insights into their theoretical behavior and stability. We use a null zero complexity factor to find the wormhole shape function for Model I. Additionally, we solve analytically the modified field equations describing wormhole for a given choice of logarithmic redshift function, exploiting the Karmarkar condition for embedding class one metrics for Model II. To achieve this, we analyze the wormhole geometry in a static spherical spacetime with an anisotropic matter configuration. The study investigates a number of parameters, including density, energy conditions, equation of state parameter, adiabatic sound velocity, and equilibrium condition. The solution shows a traversable wormhole that violates the null energy criterion and equilibrium state for certain ranges of free parameters. We employ adiabatic sound velocity analysis to concentrate on the stability of the wormhole. Furthermore, by using the equation of state parameter (ω), we conclude that both models end up in the phantom dark energy region. Finally, our findings highlight distinct photon deflection behaviors in dRTG massive gravity, with Model II showing negative angles indicative of repulsive gravity, while Model I exhibits positive angles, underscoring significant differences in gravitational dynamics.