Traversable wormholes in the extended teleparallel theory of gravity with matter coupling

TL;DR

This paper investigates traversable wormhole solutions within the extended $f( au,T)$ gravity framework, incorporating Gaussian and Lorentzian noncommutative geometries, and analyzes their stability, energy conditions, and structural properties.

Contribution

It introduces exact wormhole solutions in $f( au,T)$ gravity with noncommutative geometries, highlighting their stability and potential physical viability, which is novel in this modified gravity context.

Findings

Wormhole solutions violate weak energy condition.

Solutions are stable under equilibrium analysis.

Embedded diagrams illustrate wormhole structures.

Abstract

This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the $f(\tau, T)$ gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within $f(\tau,T)$ gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions.