On possible wormhole solutions supported by non-commutative geometry within $f(R, L_m)$ gravity

TL;DR

This paper investigates traversable wormhole solutions supported by non-commutative geometry within the $f(R,L_m)$ gravity framework, analyzing their properties, energy conditions, and stability through graphical and theoretical methods.

Contribution

It introduces new wormhole solutions in $f(R,L_m)$ gravity with non-commutative geometry using Gaussian and Lorentzian distributions, and examines their stability and energy conditions.

Findings

Derived shape functions satisfying wormhole properties

Analyzed energy conditions and exotic matter nature

Studied stability via speed of sound and TOV equation

Abstract

Non-commutativity is a key feature of spacetime geometry. The current article explores the traversable wormhole solutions in the framework of $f(R,L_m)$ gravity within non-commutative geometry. By using the Gaussian and Lorentzian distributions, we construct tideless wormholes for the nonlinear $f(R,L_m)$ model $f(R,L_m)=\dfrac{R}{2}+L_m^\alpha$. For both cases, we derive shape functions and discuss the required different properties with satisfying behavior. For the required wormhole properties, we develop some new constraints. The influence of the involved model parameter on energy conditions is analyzed graphically which provides a discussion about the nature of exotic matter. Further, we check the physical behavior regarding the stability of wormhole solutions through the TOV equation. An interesting feature regarding the stability of the obtained solutions via the speed of sound parameters within the scope of average pressure is discussed. Finally, we conclude our results.