Abstract
Solutions of the Maxwell equations for electrostatic systems with manifestly vanishing electric currents in the curved space-time for stationary metrics are shown to exhibit a non-vanishing magnetic field of pure geometric origin. In contrast to the conventional magnetic field of the Earth it can not be screened away by a magnetic shielding. As an example of practical significance we treat electrostatic systems at rest on the rotating Earth and derive the relevant geometric magnetic field. We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings.
Highlights
We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings
We have shown that in the pure electrostatic systems at rest on the rotating bodies there can exist a geometric magnetic field
From the general relativity point of view, it originates from the nonvanishing off-diagonal elements g0i of the metric tensor which are proportional to the angular velocity of rotation of the gravitating body
Summary
The local coordinates are denoted as xμ, μ = 0, 1, 2, 3 = (0, i), i = 1, 2, 3. Let the electromagnetic field (2-form) be expressed through 4-potential Aμ (1-form) in local coordinates as: Fμν = ∂μAν − ∂ν Aμ. The field (2.1) is a holonomic one. We have the inhomogeneous Maxwell equations in the local coordinates:. −g g ≡ det gμν , F μν = gμλgνρFλρ. The electric and magnetic fields in ONB are defined by the usual rules (see appendix D): Eα = F α0 = eαμe0ν F μν = eαi e00F i0 + eαi e0j F ij , εαβγ Hγ = −F αβ = −eαμeβν F μν , ε123 = 1
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