Rankine-Hugoniot Relations in Relativistic Combustion Waves

TL;DR

This paper analyzes relativistic Rankine-Hugoniot relations for combustion waves, revealing unique shock behaviors and rare phenomena like negative-pressure flows, with implications for astrophysics and dark energy understanding.

Contribution

It extends classical shock relations into the relativistic regime, exploring their implications for astrophysical phenomena and identifying conditions for rare shock types.

Findings

Negative-pressure downstream flows in relativistic shocks

Existence of rarefaction shocks with adiabatic index < 1

Weak detonations and strong deflagrations are more common in astrophysics

Abstract

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.