The quantization of gravity

• Verfasst von: Gerhardt, Claus [VerfasserIn]
• Titel: The quantization of gravity
• Titelzusatz: the quantization of the full Einstein equations
• Verf.angabe: Claus Gerhardt
• E-Jahr: 2023
• Jahr: 17 August 2023
• Umfang: 34 S.
• Fussnoten: Gesehen am 22.08.2023
• Titel Quelle: Enthalten in: Symmetry
• Ort Quelle: Basel : MDPI, 2009
• Jahr Quelle: 2023
• Band/Heft Quelle: 15(2023), 8, Artikel-ID 1599, Seite 1-34
• ISSN Quelle: 2073-8994
• DOI: doi:10.3390/sym15081599
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: black hole
• Sach-SW: entropy
• Sach-SW: negative cosmological constant
• Sach-SW: partition function
• Sach-SW: quantization of gravity
• Sach-SW: quantum gravity
• Sach-SW: spatial eigenfunctions
• Sach-SW: temporal eigenfunctions
• K10plus-PPN: 1857211936

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.