The quantization of gravity: The quantization of the full Einstein equations

Abstract

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.

Feature Paper https://www.mdpi.com/2073-8994/15/8/1599

References in corpus (2)

• Quantum cosmological Friedman models with an initial singularity
• The quantization of gravity: Quantization of the Hamilton equations

Cited by in corpus (1)

• Extending the solutions and the equations of quantum gravity past the big bang singularity