  We investigate the properties of a degenerate dilute gas of neutral fermionic
particles in a harmonic trap that interact via dipole-dipole forces. We employ
the semiclassical Thomas-Fermi method and discuss the Dirac correction to the
interaction energy. A nearly analytic as well as an exact numerical
minimization of the Thomas-Fermi-Dirac energy functional are performed in order
to obtain the density distribution. We determine the stability of the system as
a function of the interaction strength, the particle number, and the trap
geometry. We find that there are interaction strengths and particle numbers for
which the gas cannot be trapped stably in a spherically symmetric trap, but
both prolate and oblate traps will work successfully.
