Study of Static Wormhole Solutions in $F(T,T_\mathcal{G})$ Gravity

TL;DR

This paper explores static wormhole solutions within $F(T,T_ ext{G})$ gravity, demonstrating that such solutions can exist without exotic matter under certain conditions and analyzing their stability and energy conditions.

Contribution

It introduces specific wormhole solutions in $F(T,T_ ext{G})$ gravity considering various matter contents and examines their physical viability and stability.

Findings

Wormhole solutions without exotic matter are possible in certain spacetime regions.

Energy conditions are satisfied for some matter configurations.

Stable wormhole solutions exist for anisotropic, isotropic, and traceless fluids.

Abstract

In this paper, we investigate static spherically symmetric wormhole solutions in the background of $F(T,T_\mathcal{G})$ gravity ($T$ is the torsion scalar and $T_{\mathcal{G}}$ represents teleparallel equivalent of the Gauss-Bonnet term). We study the wormhole solutions by assuming four different matter contents, a specific redshift function and a particular $F(T,T_\mathcal{G})$ model. The behavior of null/weak energy conditions for these fluids is analyzed graphically. It turns out that wormhole solutions can be obtained in the absence of exotic matter for some particular regions of spacetime. We also explore stability of wormhole solutions through equilibrium condition. It is concluded that there exist physically acceptable wormhole solutions for anisotropic, isotropic and traceless fluids.