Einstein clusters as dark matter fluid-like models for constructing new wormhole solutions in f(R,Lm,T) gravity

Abstract

This study explores traversable wormholes in $f(R,L_m,T)$ gravity, which modifies traditional gravity by integrating the matter Lagrangian and the trace of the energy-momentum tensor. We define this modification as $f(R,L_m,T)=R+\lambda L_m+\chi T$, where λ and χ are coupling constants. Focusing on $L_m=-\rho$, where ρ represents the energy density and a constant redshift function $\hat{\nu }\left(r\right)$, we investigate the properties and gravitational lensing of Einstein clusters, formed by weakly interacting massive particles as dark matter halos. These clusters exhibit tangential pressure dominance, characterized by an equation of state where the tangential pressure $P_t$ is proportional to the energy density ρ (i.e., $P_t=\sigma \rho$, where σ is a constant), which can adjust anisotropy to model galactic rotation curves effectively. We derive the shape function under the influence of Einstein clusters and analyze the null energy condition's effect on matter distribution in anisotropic fluids. The stability of the resulting wormhole solutions is confirmed via the Tolman-Oppenheimer-Volkoff formalism. Our analysis of photon deflection along null geodesics shows that for σ in the range $[0,0.25]$, the deflection angle is negative, causing photons to bend outward. In contrast, for σ in the range $[-0.25,0]$, the angles are positive, indicating that light rays curve inward toward the wormhole throat.