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Classical and Quantum Singularities of Levi-Civita Spacetimes with and without a Positive Cosmological Constant

D. A. Konkowski·C. Reese·T. M. Helliwell·C. Wieland
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Abstract

Levi-Civita spacetimes have classical naked singularities. They also have quantum singularities. Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is said to be quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint on a $C_{0}^{\infty}$ domain in $L^{2}$, a Hilbert space of square integrable functions. Here we summarize how Weyl's limit point-limit circle criterion can be used to determine whether a wave operator is essentially self-adjoint and how this test can then be applied to scalar wave packets in Levi-Civita spacetimes with and without a cosmological constant to help elucidate the physical properties of these spacetimes.

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D. A. Konkowski, C. Reese, T. M. Helliwell, C. Wieland. 2004-10-21. Classical and Quantum Singularities of Levi-Civita Spacetimes with and without a Positive Cosmological Constant. https://arxiv.org/abs/gr-qc/0410114

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