  The gravitational path integral is usually implemented with a covariant
action by analogy with other gauge field theories, but the gravitational case
is different in important ways. A key difference is that the integrand has an
essential singularity, which occurs at zero lapse where the spacetime metric
degenerates. The lapse integration contour required to impose the local time
reparametrization constraints must run from $-\infty$ to $+\infty$, yet must
not pass through zero. This raises the question: what is the correct
integration contour, and why? We study that question by starting with the
reduced phase space path integral, which involves no essential singularity. We
observe that if the momenta are to be integrated before the lapse, to obtain a
configuration space path integral, the lapse contour should pass below the
origin in the complex lapse plane. This contour is also consistent with the
requirement that quantum field fluctuation amplitudes have the usual short
distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy
from a Lorentzian path integral. We close with a discussion of related issues,
including potential obstacles to deriving a nonperturbative covariant
gravitational path integral.
