Quantum fate of timelike naked singularity with scalar hair

Abstract: We study the quantum fate of a naked curvature singularity sourced by a scalar field via several methods and compare the results obtained. The first method relies on relativistic quantum mechanics on a fixed background employing the Klein--Gordon and the Dirac equations for a static spacetime. We show that both the Klein--Gordon and the Dirac particles feel this singularity therefore this method does not provide its resolution. For comparison, we subsequently employ methods for quantizing the geometry itself. We selected the canonical quantization via conditional symmetries and as a last approach we use a maximal acceleration derivation in the covariant loop quantum gravity. In both of these approaches the singularity is resolved at the quantum level. We discuss these conflicting results bearing in mind that quantum particles probe classical geometry in the first approach while the last two methods quantize the geometry itself.