  The synchronous gauge in gravity ($g_{0 \lambda} = - \delta_{0 \lambda}$) is
ill-defined due to the singularity at $p_0 = 0$ in the graviton propagator.
Previously we studied "softening" this gauge by considering instead the gauge
$n^\lambda g_{\lambda \mu} = 0$, $n^\lambda = (1, - \varepsilon (\partial^j
\partial_j )^{- 1} \partial^k ) $ in the limit $\varepsilon \to 0$. We now
explore the possibility of using a principal value prescription (not in the
standard Cauchy sense), which amounts, roughly speaking, to replacing
singularities $p_0^{-j} \Rightarrow [ (p_0 + i \varepsilon )^{-j} + (p_0 - i
\varepsilon )^{-j} ] / 2$, which then behave like distributions. We show that
such a propagator follows upon adding to the action a gauge-violating term of a
general form, which reduces to $ \sim \int f_\lambda \Lambda^{\lambda \mu}
f_\mu \d^4 x $ with a constant operator $\Lambda^{\lambda \mu}$ depending on
$\partial$ and a metric functional $f_\lambda$. The contribution of
Faddeev-Popov's ghosts to the effective action is analysed. For the required
intermediate regularization, the discrete structure of the theory at small
distances is implied. It is shown that the ghost contribution can be
disregarded in the limit $ \varepsilon \to 0$.
