Covariant disturbances and exceptional waves

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Abstract
The disturbances of a field are determined for each kind of wave by the hyperbolic field equations. In a space-time formulation one may consider tensors which also depend on the 4-normal to the wavefront. It is shown that the disturbance of such a tensor has a definite covariant form only when the wave is exceptional. For the sake of illustration a perfect fluid is considered. It appears that the sound waves are exceptional not only when the fluid is incompressible but also when a special equation of state is used. This relation between pressure and density corresponds in the nonrelativistic limit to a usual approximation for subsonic flow.

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