Viable embedded wormholes and energy conditions in $f(\mathcal{R},\mathcal{G})$ gravity

TL;DR

This paper investigates embedded wormhole solutions within $f( ext{R}, ext{G})$ gravity, analyzing energy conditions and the necessity of exotic matter, and presents graphical results for different model parameters.

Contribution

It introduces generalized embedded wormhole solutions in $f( ext{R}, ext{G})$ gravity and analyzes their energy conditions with respect to anisotropic matter sources.

Findings

Energy conditions are graphically analyzed for different parameters.

Regions where energy conditions are violated indicate the presence of exotic matter.

The study provides specific parameter ranges where wormholes are viable without exotic matter.

Abstract

The current study explores the generalized embedded wormhole solutions in the background of $f(\mathcal{R},\mathcal{G})$ gravity, where $\mathcal{R}$ represents the Ricci scalar and $\mathcal{G}$ denotes the Gauss-Bonnet invariant. To investigate the necessary structures of the wormhole solutions we thoroughly analyzed the energy conditions under $f(\mathcal{R},\mathcal{G})$ gravity within the anisotropic source of matter. To meet this aim, we consider spherically symmetric geometry with the most generic gravity model of the gravity. A modified version of the field equations is calculated for two different embedded wormhole solutions. All the energy conditions are calculated and shown graphically with the regional ranges of the model parameter. Further, the invalid region of the energy conditions confirms the presence of exotic matter. Finally, we have concluding remarks.