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PROPAGATION OF SIGNALS IN SPACES
WITH AFFINE CONNECTIONS AND METRICS
AS MODELS OF SPACE-TIME
S. Manoff
The propagation of signals in space-time is considered on the
basis of the notion of null (isotropic) vector field in spaces with affine
connections and metrics ((`Ln,g) spaces) as models of space or
space-time. The Doppler effect is generalized for this type of spaces. The
notions of the aberration, standard (longitudinal) Doppler effect, and
transversal Doppler effect are introduced. On their grounds, the Hubble effect
appears as the Doppler effect with explicit forms of the centrifugal
(centripetal)
and Coriolis velocities and accelerations in spaces with affine connections
and metrics. The Doppler effect, Hubble effect and aberration could be used in
mechanics of continuous media and in other classical field theories in the
same way as a standard Doppler effect is used in classical and relativistic
mechanics.
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