Charge and the topology of spacetime

Diemer, Tammo; Hadley, Mark J

doi:10.1088/0264-9381/16/11/308

Cited by 12 publications

(26 citation statements)

References 4 publications

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“…We now stay with the same scenario as in the previous section, but instead apply the bound current version of Maxwell theory as given by (15), interpreting J b as representing the polarisation of the vacuum. It is known from quantum field theory that vacuum polarization occurs naturally for intense fields, with the first order correction to the excitation 2-form given by (6).…”

Section: Polarisation Of the Vacuummentioning

confidence: 99%

Evaporating Black-Holes, Wormholes, and Vacuum Polarisation: Must they Always Conserve Charge?

2019

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A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials ϕ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth. * https://orcid.org/0000-0003-1597-6084; j.gratus@lancaster.ac.uk † https://orcid.org/0000-0001-5744-8146; Dr.Paul.Kinsler@physics.org ‡ https://orcid.org/0000-0003-0643-7169; m.mccall@imperial.ac.uk arXiv:1904.04103v1 [gr-qc] 8 Apr 2019 III IV L i g h t c o n e J f = 0 J b = 0 J f = 0 J b = 0 J f = 0 J b = 0 J f = 0 J b = 0 J b = 0 J f = 0 FIG. 5: Domains in a spacetime M where J f (blue) and J b (red) may be non-zero; note in particular that the supports of J f and J b do not intersect. For completeness, we show several different regions where the various possible combinations of zero and non-zero J f and J b hold, although alternative (and simpler) scenarios are possible. Note that Region I matches the cone shown on fig. 4, and Region IV encompasses both a section above the light line, as well as below.

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Section: Polarisation Of the Vacuummentioning

confidence: 99%

Evaporating Black-Holes, Wormholes, and Vacuum Polarisation: Must they Always Conserve Charge?

2019

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“…Wormholes can be constructed with any combination of time and space orientability [5], and by a similar process monopole type structures of any orientation can be described [6]. The Möbius strip is non-orientable and if the central circle is considered to be a space dimension, and the other direct a time direction, then the Möbius strip models a 1 + 1 dimensional spacetime that is space orientable but not time orientable.…”

Section: Interactions and Topology Changementioning

confidence: 99%

“…However a 4-geon that is not time orientable does not have a consistently defined normal vector and the divergence theorem fails, allowing the appearance of net electric charge. A mathematical treatment in arbitrary dimensions is given in [6].…”

Section: Orientability and Chargementioning

confidence: 99%

A gravitational explanation for quantum theory — non-time-orientable manifolds

Hadley¹

2007

AIP Conference Proceedings

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Causally simple inextendible spacetimes are hole-free J. Math. Phys. 53, 062501 (2012) Spherical linear waves in de Sitter spacetime J. Math. Phys. 53, 052501 (2012) Factorization method in scalar field on AdS3 in spherical coordinates J. Math. Phys. 53, 053502 (2012) Asymptotic stability of vacuum twisting type II metrics Abstract. Spacetime manifolds that are not time orientable play a key role in a gravitational explanation of quantum theory. Such manifolds allow topology change, but also have fascinating additional properties such as net charge from source-free equations and spin half transformation properties. It is shown how the logical structure of propositions and the probabilities of quantum theory arise from such acausal space times.

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“…Although this paper is entirely classical, the lack of a time orientation gives new results and is motivated by earlier work linking spacetimes that are not time orientable with foundations of quantum theory [4,5], the existence of electric charges [6], and spin half transformations of elementary particles [7].…”

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confidence: 99%

Electrodynamics and Time Orientability

Hadley

2017

Int J Theor Phys

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On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell's equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path. The boundary of a time reversing region can therefore have a net electric flux and appear exactly as a region containing an electric charge. The treatment is purely classical, but motivated by links between acausal structures and quantum theory.

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Charge and the topology of spacetime

Cited by 12 publications

References 4 publications

Evaporating Black-Holes, Wormholes, and Vacuum Polarisation: Must they Always Conserve Charge?

Evaporating Black-Holes, Wormholes, and Vacuum Polarisation: Must they Always Conserve Charge?

A gravitational explanation for quantum theory — non-time-orientable manifolds

Electrodynamics and Time Orientability

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