Surface tension of quark matter in a geometrical approach

The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects, because it determines the nucleation rate and the associated critical size. However, this quantity is not well known and the theoretical estimates fall within a wide range, ${\gamma }_0\approx 5–300\mathrm{MeV}/{\mathrm{fm}}^2$. We show here that once the equation of state is available one may use a geometrical approach to obtain a numerical value for the surface tension that is consistent with the model approximations adopted. We illustrate this method within the two-flavor linear $\sigma$ model and the Nambu–Jona-Lasinio model with two and three flavors. Treating these models in the mean-field approximation, we find ${\gamma }_0\approx 7–30\mathrm{MeV}/{\mathrm{fm}}^2$. Such a relatively small surface tension would favor the formation of quark stars and may thus have significant astrophysical implications. We also investigate how the surface tension decreases towards zero as the temperature is raised from zero to its critical value.