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

Claus Gerhardt Ruprecht-Karls-Universit├Ąt

Mathematical Physics Theoretical Physics mathscidoc:2307.22001

Symmetry, 15, (8), 1599, 2023.8
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 $\R[]_+$. In case $n\ge 17$ and provided the cosmological constant $\Lam$ 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.
quantization of gravity, quantum gravity, black hole, negative cosmological constant, partition function, entropy, temporal eigenfunctions, spatial eigenfunction
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@inproceedings{claus2023the,
  title={The quantization of gravity: The quantization of the full Einstein equations},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20230727012223921345752},
  booktitle={Symmetry},
  volume={15},
  number={8},
  pages={1599},
  year={2023},
}
Claus Gerhardt. The quantization of gravity: The quantization of the full Einstein equations. 2023. Vol. 15. In Symmetry. pp.1599. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20230727012223921345752.
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