Formation of stable wormhole solution with non-commutative geometry in the framework of $f(R,\mathcal{L}_m, T)$ gravity

Abstract

This research delves into the potential existence of traversable wormholes (WHs) within the framework of $f(R,\mathcal{L}_m, T)$ gravity, a modification that includes the matter Lagrangian and the trace of the energy-momentum tensor with specific coupling strengths $\alpha$ and $\beta$. A thorough examination of WH solutions is undertaken using a constant redshift function in tandem with a linear $f(R,\mathcal{L}_m, T)$ model. The analysis involves deriving WH shape functions based on non-commutative geometry, with a particular focus on Gaussian and Lorentzian matter distributions $\rho$. Constraints on the coupling parameters are developed so that the shape function satisfies both the flaring-out and asymptotic flatness conditions. Moreover, for positive coupling parameters, violating the null energy condition (NEC) at the WH throat $r_0$ demands the presence of exotic matter. For negative couplings, however, we find that exotic matter can be avoided by establishing the upper bound $\beta+\alpha/2<-\frac{1}{\rho r_0^2}-8\pi$. Additionally, the effects of gravitational lensing are explored, revealing the repulsive force of our modified gravity for large negative couplings. Lastly, the stability of the derived WH solutions is verified using the Tolman-Oppenheimer-Volkoff (TOV) formalism.