Traversable wormhole solutions in the f (R) theories of gravity under the Karmarkar condition* *The fourth author would like to express their gratitude to the Deanship of Scientific Research at King Khalid University, Saudi Arabia, for providing a funding research group under the research grant R.G.P2/130/43. The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project

Abstract

This paper examines traversable wormhole models in the theories of gravity by applying the Karmarkar condition. For this purpose, we consider spherically symmetric space-time to examine the structure of wormholes. First, we investigate wormholes and their geometry using the redshift function under various conditions. Subsequently, we discuss the embedding diagram of the upper and lower universe using radial coordinates in two and three-dimensional Euclidean affine space. Three exclusive models are considered for the theories of gravity, and the radial and tangential pressures are observed. Furthermore, by taking a definite shape function, we observe the behavior of energy conditions. We determine that energy conditions are violated, and their violation is generic and represents the presence of exotic matter. According to Einstein's field theory, the existence of wormholes is predicated on the occurrence of rare material. Hence, we conclude that our study is more realistic and stable.