Schmitz, Tim 
ORCID: 0000-0002-2822-2794
(2021).
Bouncing Black Holes From Canonical Quantum Gravity.
PhD thesis, Universität zu Köln.
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Abstract
It is commonly believed that the ubiquitous singularities of general relativity will be cured in a theory of quantum gravity. In the absence of a complete such theory, one can still employ reduced toy models to investigate how an avoidance of singularities could be facilitated. One particular scenario for this is bouncing gravitational collapse: in it, quantum gravitational effects prevent the matter from fully collapsing to a singularity, and instead cause it to re-expand. In the discussion of such bounces two aspects turn out to be of particular importance. First, the bounce necessitates quantum corrections not only in the high curvature region, but also at the horizon. The question is then how the behavior of the horizon is modified to accommodate the bounce. Second, since the `black hole' is not the end result of the collapse anymore but an intermediate state, its finite lifetime is crucial as a consistency check for bouncing collapse models. In this thesis we construct and explore such models, especially with regard to these aspects. We present a quantization of the marginally bound Lema\^{i}tre-Tolman-Bondi model for inhomogeneous, spherically symmetric dust collapse, in which the model is split up into individual shells of dust and reassembled after quantization. We show that this leads to singularity avoidance via a bounce, a result that proves to be fairly robust under the quantization ambiguities. The problem is explicitly formulated from the point of view of an observer comoving with the dust, which avoids some notorious conceptual issues of quantum gravity but limits investigations of horizon behavior and lifetime. In order to go beyond these limitations, we construct a marginally bound quantum Oppenheimer-Snyder model in which both the comoving observer and an observer exterior to the collapsing matter are included. In preparation for this, we present a phase space formulation of the classical Oppenheimer-Snyder model. %We pay attention in particular to the boundary terms arising on the surface of the dust cloud. The switch between the two observers is implemented by promoting the transformation between their adapted coordinates to a canonical transformation. Due to the complicated functional form of the Hamiltonian for the exterior observer an integral quantization method is used, namely affine coherent states quantization, and we focus on the investigation of quantum corrected phase space dynamics. For both observers a bounce emerges. However, for the exterior observer the minimal radius of the bounce is so large that no horizon forms. Finally, we investigate what exterior geometries can be matched classically to a bouncing dust cloud. In particular, we show that static exteriors necessarily have a more involved causal structure, and we discuss a specific dynamic exterior in which the horizon retracts into the collapsing body at the moment of the bounce. The black hole lifetime for the latter turns out to be proportional to the mass of the cloud, and we argue that this result also applies to a larger class of dynamic exteriors.
| Item Type: | Thesis (PhD thesis) | ||||||||
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| URN: | urn:nbn:de:hbz:38-538530 | ||||||||
| Date: | 2 November 2021 | ||||||||
| Language: | English | ||||||||
| Faculty: | Faculty of Mathematics and Natural Sciences | ||||||||
| Divisions: | Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics | ||||||||
| Subjects: | Physics | ||||||||
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| Date of oral exam: | 19 October 2021 | ||||||||
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/53853 |
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