  We quantized the full Einstein equations in a globally hyperbolic spacetime
$N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation
in a fiber bundle $E$ which can be expressed as a product of spatial
eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial
eigenfunctions form a basis in an appropriate Hilbert space while the temporal
eigenfunctions are solutions to a second order ordinary differential equation
in $\mathbb{R}_+$. In case $n\ge 17$ and provided the cosmological constant
$\Lambda$ is negative the temporal eigenfunctions are eigenfunctions of a
self-adjoint operator $\hat H_0$ such that the eigenvalues are countable and
the eigenfunctions form an orthonormal basis of a Hilbert space.
