Exploring Stable Traversable Wormholes in Modified Gravity Models

Recent research by Niklas Loewer, Moreshwar Tayde, and P.K. Sahoo explores the potential for stable traversable wormholes within the framework of modified gravity, specifically $f(R,\mathcal{L}_m, T)$ gravity. This model incorporates the matter Lagrangian and the trace of the energy-momentum tensor, introducing coupling strengths denoted as (\alpha) and (\beta). The study employs a constant redshift function alongside a linear $f(R,\mathcal{L}_m, T)$ model to derive wormhole shape functions based on non-commutative geometry, focusing on Gaussian and Lorentzian matter distributions.

Key findings include the establishment of constraints on the coupling parameters to ensure that the shape function meets the necessary conditions for flaring-out and asymptotic flatness. The researchers note that for positive coupling parameters, violating the null energy condition at the wormhole throat requires the presence of exotic matter. Conversely, negative couplings allow for the avoidance of exotic matter under specific upper bounds.

Additionally, the effects of gravitational lensing were examined, revealing a repulsive force in the modified gravity model for large negative couplings. The stability of the derived wormhole solutions was confirmed using the Tolman-Oppenheimer-Volkoff formalism, which is crucial for understanding the conditions under which these theoretical structures could exist.

This research contributes to the ongoing discourse in theoretical physics regarding the nature of wormholes and their implications for our understanding of spacetime and gravity. The full paper can be accessed at arXiv:2409.04172.