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Register a new userConstruction of test Maxwell fields with scale symmetry
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Authors
Takahisa Igata
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Geometrical symmetry in a spacetime can generate test solutions to the Maxwell equation. We demonstrate that the source-free Maxwell equation is satisfied by any generator of spacetime self-similarity---a proper homothetic vector---identified with a vector potential of the Maxwell theory. The test fields obtained in this way share the scale symmetry of the background.
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We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(boldsymbol{g},boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of Lagrangian theories including both modified gravities and (possibly non-minimally coupled) modified electrodynamics. Specifically, both $boldsymbol{g}$ and $boldsymbol{F}$ are fields with vanishing scalar invariants and further satisfy two simple tensorial conditions. They describe a family of gravitational and electromagnetic plane-fronted waves of the Kundt class and of Weyl type III (or more special). The local form of $(boldsymbol{g},boldsymbol{F})$ and a few examples are also provided.
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The classical electromagnetic and gravitomagnetic fields in the vacuum, in (3+2) dimensions, described by the Maxwell-Nordstrom equations, are quantized. These equations are rederived from the field tensor which follows from a five-dimensional form of the Dirac equation. The electromagnetic field depends on the customary time t, and the hypothetical gravitomagnetic field depends on the second time variable u. The total field energy is identified with the component T44 of the five-dimensional energy-stress tensor of the electromagnetic and gravitomagnetic fields. In the ground state, the electromagnetic field and the gravitomagnetic field energies cancel out. The quanta of the gravitomagnetic field have spin 1.
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