Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-10-21
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, no figures, submitted to Proceedings of the Workshop on Dynamics and Thermodynamics of Blackholes and Naked Singular
Scientific paper
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.
Helliwell Thomas M.
Konkowski Deborah A.
Reese C. C.
Wieland C.
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