Neutrinos in cylindrically−symmetric spacetimes

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Abstract
An exact solution to the Einstein−Dirac equations is presented for a static, cylindrically−symmetric spacetime. The neutrino field is nonzero and corresponds to a neutrino current in the radial direction. The neutrinos yield a zero energy−momentum tensor and therefore the gravitational field is the same as for the vacuum case. The neutrinos in these static cylindrically−symmetric spacetimes can exist only if the spacetimes are locally equivalent to static plane−symmetric spacetimes. This type of ’’ghost neutrino’’ solution is already known to exist in plane−symmetric spacetimes.

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