Existence of Wormhole Solutions in $f(Q,T)$ Gravity under Non-commutative Geometries

TL;DR

This study explores spherically symmetric wormhole solutions within $f(Q,T)$ gravity under non-commutative geometries, analyzing models analytically and numerically, and examining energy conditions and gravitational lensing effects.

Contribution

It presents new analytic and numerical wormhole solutions in $f(Q,T)$ gravity with non-commutative geometries, including analysis of energy conditions and lensing behavior.

Findings

Shape function satisfies flare-out conditions.

NEC is violated at the wormhole throat.

Deflection angle diverges at the throat.

Abstract

In this paper, we have systematically discussed the existence of the spherically symmetric wormhole solutions in the framework of $f(Q,\,T)$ gravity under two interesting non-commutative geometries such as Gaussian and Lorentzian distributions of the string theory. Also, to find the solutions, we consider two $f(Q,\,T)$ models such as linear $f(Q,\,T)=\alpha\,Q+\beta\,T$ and non-linear $f(Q,\,T)=Q+\lambda\,Q^2+\eta\,T$ models in our study. We obtained analytic and numerical solutions for the above models in the presence of both non-commutative distributions. We discussed wormhole solutions analytically for the first model and numerically for the second model and graphically showed their behaviors with the appropriate choice of free parameters. We noticed that the obtained shape function is compatible with the flare-out conditions under asymptotic background. Further, we checked energy conditions at the wormhole throat with throat radius $r_0$ and found that NEC is violated for both models under non-commutative background. At last, we examine the gravitational lensing phenomenon for the precise wormhole model and determine that the deflection angle diverges at the wormhole throat.