Comment on "Tidal Love numbers of neutron and self-bound quark stars"

We comment on the paper of S. Postnikov et al. in Phys. Rev. D 82, 024016 (2010) and give a modified formula that needs to be taken into account when calculating the tidal Love number of neutron stars in case a first order phase-transition occurs at non-zero pressure. We show that the error made when using the original formula tends to zero as $p \rightarrow 0$ and we estimate the maximum relative error to be $\sim 5\%$ if the density discontinuity is at larger densities.