Alumina‐calcia fibers with>50% alumina and 100% alumina fibers cannot be drawn from the melt, or conventionally melt spun, because the viscosities are too low. They can, however, be spun by inviscid melt spinning, an experimental process whereby a molten jet with a viscosity of<1 Pa.s is ejected into propane, a chemically reactive medium. The pyrolytic decomposition of propane stabilizes the molten jet. The consolidated fiber that results has a carbon‐rich skin and usually, i.e., under most process conditions, but not always, a black carbon sheath. This paper identifies the chemistry and morphology of both skin and sheath by depth profile analysis, evaluates potential jet stabilization mechanisms, and concludes that the operative mechanism is rheology‐dominated. Incorporation of particulate carbon in the skin of the jet increases its surface viscosity, prevents breakup into Rayleigh waves and droplets, and facilitates melt spinning of continuous fila