Hadron-quark combustion in dense matter is a central topic in the study of phases in compact stars and their high-energy astrophysics. We critically reviewed the literature on hadron-quark combustion, dividing them into a “first wave” that treats the problem as a steady-state burning with or without constraints of mechanical equilibrium, and a “second wave” which uses numerical techniques to resolve the burning front and solves the underlying partial differential equations for the chemistry of the burning front under less restrictive conditions. We detailed the inaccuracies that the second wave amends over the first wave and highlight crucial differences between various approaches in the second wave. We also include results from time-dependent simulations of the reaction zone that include a hadronic EOS, neutrinos, and self-consistent thermodynamics without using parameterized shortcuts.
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