Wormhole Geometry and Three-Dimensional Embedding in Extended Symmetric Teleparallel Gravity

TL;DR

This paper investigates traversable wormhole solutions within extended symmetric teleparallel gravity, analyzing different models and shape functions, and visualizing their geometry through embedding diagrams to understand their structure.

Contribution

It introduces new wormhole solutions in extended symmetric teleparallel gravity with matter coupling, exploring both linear and non-linear models and their geometric properties.

Findings

Wormhole solutions are found for both linear and non-linear gravity models.

Shape functions satisfy physical and geometric conditions for traversability.

Embedding diagrams illustrate the wormhole geometries effectively.

Abstract

In the present manuscript, we study traversable wormhole solutions in the background of extended symmetric teleparallel gravity with matter coupling. With the anisotropic matter distribution we probe the wormhole geometry for two different gravity models. Primarily, we consider the linear model $ f(Q,T) =Q + 2 \, \xi \,T$. Firstly, we presume a logarithmic form of shape function and analyze the scenario for different redshift functions. Secondly, for a specific form of energy density, we derive a shape function and note its satisfying behavior. Next, for the non-linear model $f(Q,T) = Q + \alpha ,Q^2 + \beta ,T$ and a specific shape function we examine the wormhole solution. Further, with the aid of embedding diagrams, we interpreted the geometry of wormhole models. Finally, we conclude results.