Evolving embedded traversable wormholes in [formula omitted] gravity: A comparative study

Abstract

The objective of this paper is to unveil the evolving traversable wormhole solutions within the perspective of modified f(R,G) gravity, where R is Ricci scalar and G is Gauss Bonnet term. In order to accomplish this, we develop a wormhole shape function using the Karmarkar condition for traversable static wormhole geometry, that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in two and three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current study, we choose two realistic and viable f(R,G) gravity models to discuss the wormhole geometry. For the traversable wormhole configurations the energy conditions must be satisfied at the throat. For this purpose, we check the energy conditions and observed that these conditions are satisfied near the throat of the wormhole space in modified f(R,G) gravity. Further, the intriguing part of this research is to perform a comparative analysis of the evolving wormhole geometries of our considered models with the help of three-dimensional graphical representation along with their regions. Moreover, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition. It can be observed that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the proper choice of f(R,G) gravity models. As a nutshell, we can infer that our findings fulfill all of the criterion for the presence of traversable wormhole, ensuring that our study is viable and consistent.