  Theoretical and numerical analysis of the relativistic effects on the
Richtmyer-Meshkov (RM) instability reveals new and potentially very useful
effects. We find that, in contrast with the non- relativistic case, the growth
rate of the RM instability depends strongly on the equation of state of the
fluid, opening up the possibility to infer equations of state from experimental
observations of the RM instability. As opposed to the non-relativistic case, we
also discover that, above a critical value of the fluid velocity, the growth
rate of the instability counter-intuitively decreases due to the Lorentz's
factor, and vanishes in the ultrarelativistic limit, as the speed of the
particles approaches the speed of light. Both effects might prove very useful
for leading-edge applications, such as the study of the equation of state of
quark-gluon matter, and the design of fast ignition inertial confinement fusion
(ICF) schemes. We perform a linear stability analysis to characterize the
instability, for an arbitrary equation of state, and implement numerical
simulations to study the instability in the non-linear regime, using the
equation of state of an ideal gas. Furthermore, based on the numerical results,
we propose a general expression that characterizes the long term evolution of
the instability.
