Abstract
We quantized the full Einstein equations in a globally hyperbolic spacetime N=Nn+1, n≥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 R+. In case n≥17 and provided the cosmological constant Λ is negative, the temporal eigenfunctions are eigenfunctions of a self-adjoint operator H^0 such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space.
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