Effect of Einasto spike and isothermal dark matter density profile on the geometry of wormhole in f(ℜ,Lm) gravity

In the present article, we uncover striking properties of traversable wormhole solutions generated under a newly developed $f(\Re ,L_m)$ gravitational theory. Two distinct dark matter density profiles—the Einasto spike and the Pseudo-isothermal model—are employed to demonstrate the existence of stable wormhole geometries with throat radii of 1.18 km and 1.41 km, respectively. Through a rigorous analytical and plot-based survey, we delve deeper into the exotic matter characteristics of these wormhole structures and analyze their matter content in the context of energy conditions. Impressively, both wormhole models exhibit an adiabatic index greater than 1.34 ($\Gamma >\frac{4}{3}$), indicating their inherent stability. What is more, our study of the anisotropy parameter reveals the attractive nature of these wormhole solutions, a crucial property for their potential traversability. This novel work not only broadens our understanding of modified gravity theories but also highlights the remarkable possibilities of traversable wormholes, opening up new avenues in theoretical physics and in the exploration of exotic spacetime geometries.