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

Abstract

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.

Electromagnetism, axions, and topology: A first-order operator approach to constitutive responses provides greater freedom

“…This means that there are cases where it is advantageousor even required -to write the axionic response in our way. These results are linked to related discoveries [4] enabled by removing (D, H), such as non-conservation of charge in topologically non-trivial spaces, and the treatment of charges passing through wormholes. We also remarked on the possibility of there being an additional 16 more exotic constitutive parameters, for a grand total of 55 in all.…”

“…But for a non-dispersive medium, as we consider here, the tensors (κ DE ,κ DB ,κ HE , κ HB ) have no additional dependence. The nature of the excitation fields (D, H) is very different to the electromagnetic fields (E, B), and indeed there is a debate in the literature as to whether or not they are actually physical quantities [3,4,29]. Notably, it is easy to see that Maxwell's equations are invariant by adding a gauge (φ g , A g ) to the excitation fields, with the replacements…”

“…where the extraction of the magnetic field B requires both the Levi-Civita symbol ijk and the metric g i . In this notation Maxwell's equations (4), (5) become…”

Impedance rescaling and scattering from transformation optics devices

“…Here we consider a 2D radial morphism where points with a laboratory or device coordinater are transformed so as to appear at some apparent or design position = (ˆ) r f r , just as in the T-Design for a cylindrical cloak. Within this general approach, we can describe not only cloaks but also various types of illusion and/or distortion devices, and even two universes connected by a wormhole [29] 3 . However, we keep the mathematics general so that other non-cloak morphisms are allowed by the theory presented here.…”

Maxwell’s ( D, H ) excitation fields: lessons from permanent magnets

“…The role and meaning of the Maxwell excitation fields (D D D, H H H) has been a subject of debate, with arguments for and against their independent existence and measurability [1][2][3][4][5][6]. However, a recent work has demonstrated that in certain physical circumstances, such as when a black hole forms then evaporates, (D D D, H H H) cannot be guaranteed to be uniquely defined [7]. This reduces (D D D, H H H) into the role of a gauge field for the current, meaning that there is no role for attempting to measure them.…”