Alessandro Fasse

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The final state of a spherically symmetric star always admits a singularity at its center if only gravitational effects are considered. This singularity is covered by an event horizon in most cases. However, the existence of singularities in final theory of Quantum Gravity is so far unclear. For some initial conditions to the matter distribution it is possible that the formed singularity might be temporary visible. This case is called a naked singularity and is of central interest in this thesis. Their existence implies the breakdown of General Relativity itself, since it manifests that future is unpredictable from initial data alone. Anything could form in the central singularity due to the presence of an infinitely large energy density. It was shown that initial conditions leading to naked singularities are physically meaningful and cannot be neglected. The following question arises: Are singularities an artifact of General Relativity itself and can be resolved by taking quantum mechanical effects into account? Here we show, that for a specific model containing a naked singularity, we obtain an everywhere vanishing wave function. This result can be interpreted as the avoidance of the classically allowed naked singularity. Furthermore, our toy model shows certain similarities to the Friedmann-Lemaitre-Robertson-Walker metric (FLRW metric). We show that a specific perturbation around this solution is also quantum mechanically forbidden. Our results demonstrate that canonical quantization is at least in our case capable of contributing to the ongoing debate on singularity avoidance. However, we consider only one case of a naked singularity and a result the general case of (naked) singularities still remains unclear.

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University of Cologne
Conferenceroom 1 (New building)
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