  A recent time-of-flight (TOF) expansion experiment with polarized fermionic
erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid
due to dipole-dipole interaction, thus confirming previous theoretical
predictions. Here we perform a systematic study of the ground-state properties
and TOF dynamics for trapped dipolar Fermi gases from the collisionless to the
hydrodynamic regime at zero temperature. To this end we solve analytically the
underlying Boltzmann-Vlasov equation within the relaxation-time approximation
in the vicinity of equilibrium by using a suitable rescaling of the equilibrium
distribution. The resulting ordinary differential equations for the respective
scaling parameters are then solved numerically for experimentally realistic
parameters and relaxation times that correspond to the collisionless,
collisional, and hydrodynamic regime. The equations for the collisional regime
are first solved in the approximation of a fixed relaxation time, and then this
approach is extended to include a self-consistent determination of the
relaxation time. The presented analytical and numerical results are relevant
for a detailed quantitative understanding of ongoing experiments and the design
of future experiments with ultracold fermionic dipolar atoms and molecules. In
particular, the obtained results are relevant for systems with strong
dipole-dipole interaction, which turn out to affect significantly the aspect
ratios during the TOF expansion.
