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

Authors :
Gerhardt, Claus
Source :
Symmetry 15, 1599, 2023
Publication Year :
2023

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.<br />Comment: Feature Paper https://www.mdpi.com/2073-8994/15/8/1599

Subjects

Subjects :
Physics - General Physics

Details

Database :
arXiv
Journal :
Symmetry 15, 1599, 2023
Publication Type :
Report
Accession number :
edsarx.2308.12974
Document Type :
Working Paper
Full Text :
https://doi.org/10.3390/sym15081599