Kelvin-Helmholtz instability for relativistic fluids

We reexamine the stability of an interface separating two nonmagnetized relativistic fluids in relative motion, showing that, in an appropriate reference frame, it is possible to find analytic solutions to the dispersion relation. Moreover, we show that the critical value of the Mach number, introduced by compressibility, is unchanged from the nonrelativistic case if we redefine the Mach number as M=[β∕(1-β²)1∕2][βₛ∕(1-βₛ²)1∕2]^-1, where β and βₛ are, respectively, the speed of the fluid and the speed of sound (in units of the speed of light).