Existence of stable wormholes on a noncommutative-geometric background in modified gravity

TL;DR

This paper investigates stable, traversable wormhole solutions within a modified gravity framework incorporating non-commutative geometry, providing exact and numerical models, analyzing their stability, and exploring gravitational lensing effects.

Contribution

It introduces new wormhole solutions in $f(R,T)$ gravity with non-commutative geometry, including stability analysis and gravitational lensing properties.

Findings

Wormhole solutions are stable under equilibrium conditions.

Deflection angle diverges at the wormhole throat, indicating strong gravitational lensing.

Exact and numerical solutions are obtained for different $f(R,T)$ models.

Abstract

In this paper, we discuss spherically symmetric wormhole solutions in $f(R,T)$ modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentizian distributions of string theory. For some analytic discussion, we consider an interesting model of $f(R,T)$ gravity defined by $f(R,T)=f_{1}(R)+\lambda T$. By taking two different choices for the function $f_{1}(R)$, that is, $f_{1}(R)=R$ and $f_{1}(R)=R+\alpha R^{2}+\gamma R^{n}$, we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentizian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at wormhole throat.