Influence of the cosmological constant on $\kappa$-deformed Neutron Star

We study a model of the neutron star in $\kappa$-deformed space-time in the presence of the cosmological constant ($\Lambda$). The Einstein tensor and the energy-momentum tensor are generalized to $\kappa$-deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman-Oppenheimer-Volkoff equations with the inclusion of the cosmological constant in $\kappa$-deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from $3.44M_{\odot}$ to $3.68M_{\odot}$ as $\Lambda$ varies from $10^{-10}m^{-2}$ to $10^{-15}m^{-2}$. We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as $\Lambda$ decreases.