Rankine-Hugoniot Relations in Relativistic Combustion Waves
  As a foundational element describing relativistic reacting waves of relevance
to astrophysical phenomena, the Rankine-Hugoniot relations classifying the
various propagation modes of detonation and deflagration are analyzed in the
relativistic regime, with the results properly degenerating to the
non-relativistic and highlyrelativistic limits. The existence of
negative-pressure downstream flows is noted for relativistic shocks, which
could be of interest in the understanding of the nature of dark energy. Entropy
analysis for relativistic shock waves are also performed for relativistic
fluids with different equations of state (EoS), denoting the existence of
rarefaction shocks in fluids with adiabatic index \Gamma < 1 in their EoS. The
analysis further shows that weak detonations and strong deflagrations, which
are rare phenomena in terrestrial environments, are expected to exist more
commonly in astrophysical systems because of the various endothermic reactions
present therein. Additional topics of relevance to astrophysical phenomena are
also discussed.
