In one aspect, the invention includes a reactor apparatus for pyrolyzing a hydrocarbon feedstock, the apparatus including: a reactor component comprising a refractory material in oxide form, the refractory material having a melting point of at least 2060° C. and which remains in oxide form when exposed to a gas having carbon partial pressure of 10−22 bar, an oxygen partial pressure of 10−10 bar, at a temperature of 1200° C. In some embodiments, the reactor comprises a regenerative pyrolysis reactor apparatus and in other embodiments it includes a reverse flow regenerative reactor apparatus. In other aspects, this invention includes a method for pyrolyzing a hydrocarbon feedstock using a pyrolysis reactor system comprising the step of providing in a heated region of a pyrolysis reactor system for pyrolyzing a hydrocarbon feedstock, apparatus comprising a refractory material in oxide form, the refractory material having a melting point of at least 2060° C. and that remains in oxide form when exposed to a gas having a carbon partial pressure of 10−22 bar, an oxygen partial pressure of 10−10 bar, at a temperature of 1200° C.