A note on stability of neutron star and cosmological constant

We derive the equation for pressure within a neutron star while incorporating a nonzero cosmological constant ($\Lambda$). We then examine the equilibrium configurations of neutron stars in the presence of $\Lambda$ and extend the stability theorem for stellar structures to such cases. Our analysis confirms that the equilibrium theorem remains valid even when a cosmological constant is introduced. To explore the astrophysical implications, we numerically solve the stellar structure equations for various equations of state (EOS) and analyze the resulting mass–radius ($M$-$R$) relations. While the observed value of $\Lambda$ has a negligible impact on neutron star properties, we find that for $\Lambda \ge 10^{-11}{\text{m}}^{-2}$, significant deviations in the mass and radius of neutron stars arise. This result is consistent with previous studies, highlighting the sensitivity of compact object structure to nonzero $\Lambda$ values.