  In this paper, I revisit the microcanonical partition function, or density of
states (DOS), of general relativity. By using the minisuperspace path integral
approximation, I directly calculate the $S^2 \times Disc$ topology sector of
the DOS of a (quantum) spacetime with an $S^2\times \mathbb{R}$ Lorentzian
boundary from the microcanonical path integral, in contrast with previous works
in which DOSs are derived by inverse Laplace transformation from various
canonical partition functions. Although I found there always exists only one
saddle point for any given boundary data, it does not always dominate the
possible integration contours. There is another contribution to the path
integral other than the saddle point. One of the obtained DOSs has behavior
similar to that of the previous DOSs; that is, it exhibits exponential
Bekenstein--Hawking entropy for the limited energy range $ (1-\sqrt{2/3})
<GE/R_{b}< (1+\sqrt{2/3})$, where energy $E$ is defined by the Brown--York
quasi-local energy momentum tensor and $R_{b}$ is the radius of the boundary
$S^2$. In that range, the DOS is dominated by the saddle point. However, for
sufficiently high energy, where the saddle point no longer dominates, the DOS
approaches a positive constant, different from the previous ones, which
approach zero.
