Quantum singularity of Levi-Civita spacetimes

Konkowski, D. A.; Helliwell, T. M.; Wieland, C.

doi:10.1088/0264-9381/21/1/018

Cited by 28 publications

(34 citation statements)

References 18 publications

(66 reference statements)

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“…The square integrability condition at infinity is calculated by 13) and it is found that the squared norm f i (r) 2 → ∞. This result indicates that all the asymptotic solutions of the Maxwell's equation do not belong to the Hilbert space.…”

Section: Maxwell Fieldsmentioning

confidence: 99%

Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

Gürtuğ

Halilsoy

Mazharimousavi

2014

J. High Energ. Phys.

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The formation of a naked singularity in f (R) global monopole spacetime is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r = 0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity formed in f (R) global monopole spacetime remains quantum mechanically singular when it is probed with quantum fields having different spin structures. Pitelli and Letelier (Phys. Rev. D 80 (2009) 104035) had shown that for quantum scalar (spin 0) probes the general relativistic global monopole singularity remains intact. For specific modes electromagnetic (spin 1) and Dirac field (spin 1/2) probes, however, we show that the global monopole spacetime behaves quantum mechanically regular. The admissibility of this singularity is also incorporated within the Gubser's singularity conjecture.

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Section: Maxwell Fieldsmentioning

confidence: 99%

Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

Gürtuğ

Halilsoy

Mazharimousavi

2014

J. High Energ. Phys.

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“…(63) do not belong to the Hilbert space H (we refer to the references; [46] for detailed mathematical analysis and [47][48][49][50][51][52][53][54][55][56][57][58][59][60] for applications of the HM approach in different spacetimes). This will be achieved by defining the function space on each t =constant hypersurface as H = { R| R < ∞} with the following norm given for the metric (2):…”

Section: Quantum Singularitiesmentioning

confidence: 99%

A new Einstein-nonlinear electrodynamics solution in $$2+1$$ 2 + 1 dimensions

2014

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We introduce a class of solutions in 2 + 1-dimensional Einstein-Power-Maxwell theory for a circularly symmetric electric field. The electromagnetic field is considered with an angular component given byFirst, we show that the metric for zero cosmological constant and the Power-MaxwellLagrangian of the form of F μν F μν coincides with the solution given in 2 + 1-dimensional gravity coupled with a massless, self-interacting real scalar field. With the same Lagrangian and a non-zero cosmological constant we obtain a non-asymptotically flat wormhole solution in 2 + 1 dimensions. The confining motions of massive charged and chargeless particles are investigated too. Secondly, another interesting solution is given for zero cosmological constant together with the conformal invariant condition. The formation of a timelike naked singularity for this particular case is investigated within the framework of the quantum mechanics. Quantum fields obeying the Klein-Gordon and Dirac equations are used to probe the singularity and test the quantum mechanical status of the singularity.

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“…Studies have been made of the nature of the singularity [49] and of the Dirac equation on the Levi-Civita background [50]. Many papers have considered the matching of the Levi-Civita solution to cylindrical sources, whether fluid bodies, shells or more general sources, e.g.…”

Section: This Suggests That Another Interpretation Is Needed Ifmentioning

confidence: 99%

Editorial note to: T. Levi-Civita, The physical reality of some normal spaces of Bianchi and to: Einsteinian ds 2 in Newtonian fields. IX: The analog of the logarithmic potential

MacCallum

2011

Gen Relativ Gravit

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Quantum singularity of Levi-Civita spacetimes

Cited by 28 publications

References 18 publications

Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

A new Einstein-nonlinear electrodynamics solution in $$2+1$$ 2 + 1 dimensions

Editorial note to: T. Levi-Civita, The physical reality of some normal spaces of Bianchi and to: Einsteinian ds 2 in Newtonian fields. IX: The analog of the logarithmic potential

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