Similarity Analysis for Relativistic Flow in One Dimension

Transformations and restrictions are applied to the equations of relativistic flow in one space dimension which reduce the problem to a consideration of simpler differential equations. The results are closely related to those of characteristic analysis. It is found that for cases in which one similarity variable describes the system, the fluid has constant velocity along straight lines in the $x$ , $\mathrm{ct}$ system. Two special equations of state, $\mathrm{p\hspace{0.17em}=\hspace{0.17em}}\frac{1}{3}E$ and $\mathrm{p\hspace{0.17em}=\hspace{0.17em}}\frac{1}{3}{\mathrm{(E-nmc}}^2)$ are considered in detail. Analytic results are obtained and are applied to the problem of shock propagation into a region of decreasing density.