  The most general covariant gauge fixing Lagrangian is considered for a
spin-two gauge theory in the context of the Faddeev-Popov procedure. In
general, five parameters characterize this gauge fixing. Certain limiting
values for these parameters give rise to a spin-two propagator that is either
traceless or transverse, but for no values of these parameters is this
propagator simultaneously traceless and transverse. Having a
traceless-transverse (TT) propagator ensures that only the physical degrees of
freedom associated with the tensor field propagate, and hence it is analogous
to the Landau gauge in electrodynamics. To obtain such a traceless-transverse
propagator, a gauge fixing Lagrangian which is not quadratic must be employed;
this sort of gauge fixing Lagrangian is not encountered in the usual
Faddeev-Popov procedure. It is shown that when this non-quadratic gauge fixing
Lagrangian is used, two Fermionic and one Bosonic ghost arise. As a simple
application we discuss the energy-momentum tensor of the gravitational field at
finite temperature.
