Diffusive Shock Acceleration in Unmodified Relativistic, Oblique Shocks
  We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. While known results are obtained for nonrelativistic and ultra-relativistic parallel shocks, new results are presented for the less explored trans- relativistic regime and for oblique, fully relativistic shocks. We find, for a wide trans-relativistic range extending to shock Lorentz factors >30, that the particle spectrum produced by DSA varies strongly from the canonical f(p) proportional to p^{-4.23} spectrum known to result in ultra-relativistic shocks. Trans- relativistic shocks may play an important role in gamma-ray bursts and other sources and most relativistic shocks will be highly oblique. 
Donald C. Ellison and Glen P. Double