Abstract
Considers the linearised gravitational and electromagnetic fields of an axially symmetric charged source which is rotating about its symmetry axis and moving with arbitrary acceleration along its symmetry axis when viewed in the flat background space-time. It is established that if the linearised field of the body and the linearised twist of the degenerate principal null direction of the Weyl tensor are 'wire' singularity-free, then the body must either move with zero acceleration or perform runaway motion from an unaccelerated state in the infinite past, and its mass and charge are constant at lowest order. Also, its rotation is either uniform or singular in the infinite past.
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