Non-commutative Wormholes in $f(R)$ Gravity satisfying the Energy Conditions

TL;DR

This paper demonstrates that in $f(R)$ gravity combined with non-commutative geometry, traversable wormholes can be constructed that satisfy the null energy condition, avoiding the need for exotic matter as in standard General Relativity.

Contribution

It introduces a novel approach combining $f(R)$ gravity and non-commutative geometry to realize traversable wormholes that respect energy conditions, which is not achieved in classical GR.

Findings

Wormholes respecting NEC can be obtained with suitable parameters in $f(R)$ gravity.

Non-commutative geometry allows realization of wormholes with phantom-like sources.

Energy conditions are validated for the constructed wormholes.

Abstract

Traversable wormholes in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and such behavior may be avoided in modified gravity. Moreover, the concept of non-commutative geometry as a gravitational source can be leveraged both in GR and modified gravity to realize non-trivial space-time configurations. In this study, we use $f(R)$ gravity in conjunction with non-commutative geometry to analyze spherically symmetric traversable Morris-Thorne wormhole solutions from the aspect of energy condition violation, considering both constant and variable red-shift functions. First, we use well constrained metric and model parameters in a viable $f(R)$ gravity model to demonstrate that wormholes respecting the NEC can be obtained with suitable choices of parameters. Additionally, we check the strong and dominant energy conditions to further validate our results. We then leverage non-commutative geometry in the framework of $f(R)$ gravity to show that wormholes respecting the different energy conditions with a phantom-like source can be realized with suitable choices of model parameters. Our comprehensive analyses using well-constrained model parameters show that wormholes satisfying the NEC can be realized in the framework of non-commutative geometry with modified gravity.