  We investigate the spacetime-dependent condensation of the tachyon in
effective field theories. Previous work identified singularities in the field
which appear in finite time: infinite gradients at the kinks, and (in the
eikonal approximation) caustics near local minima. By performing a perturbation
analysis, and with numerical simulations, we demonstrate and explain key
features of the condensation process: perturbations generically freeze, and
minima develop singular second derivatives in finite time (caustics). This last
has previously been understood in terms of the eikonal approximation to the
dynamics. We show explicitly from the field equations how this approximation
emerges, and how the caustics develop, both in the DBI and BSFT effective
actions. We also investigate the equation of state parameter of tachyon matter
showing that it is small, but generically non-zero. The energy density tends to
infinity near field minima with a charateristic profile. A proposal to regulate
infinities by modifying the effective action is also studied. We find that
although the infinities at the kinks are successfully regularised in the
time-dependent case, caustics still present.
