Surface tension of hot and dense quark matter under strong magnetic fields

We study the surface tension of hot, highly magnetized three-flavor quark matter droplets, focusing specifically on the thermodynamic conditions prevailing in neutron stars, hot lepton-rich protoneutron stars, and neutron star mergers. We explore the role of temperature, baryon number density, trapped neutrinos, droplet size, and magnetic fields within the multiple reflection expansion formalism (MRE), assuming that astrophysical quark matter can be described as a mixture of free Fermi gases composed of quarks $u$, $d$, $s$, electrons, and neutrinos, in chemical equilibrium under weak interactions. We find that the total surface tension is rather unaffected by the size of the drop but is quite sensitive to the effect of baryon number density, temperature, trapped neutrinos, and magnetic fields (especially above $eB\sim 5\times {10}^{-3}{\mathrm{GeV}}^2$). Surface tensions parallel and transverse to the magnetic field span values up to $\approx 25\mathrm{MeV}/{\mathrm{fm}}^2$. For $T\lesssim 100$ MeV, the surface tension is a decreasing function of temperature but above 100 MeV it increases monotonically with $T$. Finally, we discuss some astrophysical consequences of our results.