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QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA
- Date Issued:
- 2024
- Abstract/Description:
- We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions.
Title: | QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA. |
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Name(s): |
Dias, Rafael Guolo , author Engle, Jonathan S. , Thesis advisor Florida Atlantic University, Degree grantor Department of Physics Charles E. Schmidt College of Science |
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Type of Resource: | text | |
Genre: | Electronic Thesis Or Dissertation | |
Date Created: | 2024 | |
Date Issued: | 2024 | |
Publisher: | Florida Atlantic University | |
Place of Publication: | Boca Raton, Fla. | |
Physical Form: | application/pdf | |
Extent: | 92 p. | |
Language(s): | English | |
Abstract/Description: | We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions. | |
Identifier: | FA00014546 (IID) | |
Degree granted: | Dissertation (PhD)--Florida Atlantic University, 2024. | |
Collection: | FAU Electronic Theses and Dissertations Collection | |
Note(s): | Includes bibliography. | |
Subject(s): |
Black holes (Astronomy) Quantum theory Diffeomorphisms Gravity |
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Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00014546 | |
Use and Reproduction: | Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
Host Institution: | FAU |