Time evolution of a density discontinuity in the one-dimensional gravitational gas

Classical time-dependent perturbation theory is applied to the Vlassov-Poisson equations describing the one-dimensional gravitational gas. The initial conditions are an initial Maxwellian velocity distribution and a stepfunction discontinuity. It is shown that on top of the usual free-particle diffusion - smoothing out the initial density discontinuity - a density pulse and a counter-pulse propagate away from the original discontinuity. The results suggest that initial density discontinuities can seed the formation of inhomogeneities in the evolution of a collisionless one-dimensional gravitational gas, a result which should be verified in three dimensions, to study the formation of inhomogeneities in galactic dynamics