  The vibrating string is a source of gravitational waves which requires novel
computational techniques, based on the explicit construction of a conserved and
renormalized (in a classical sense) energy-momentum tensor. The renormalization
is necessary to take into account the effect of external constraints, which
affect the emission considerably. Vibrating media offer in general a testing
ground for reconciling conflicts between General Relativity and other branches
of physics; however, constraints are absent in sources like the Weber bar, for
which the standard covariant formalism for elastic bodies can also be applied.
Our solution method is based on the linearized Einstein equations, but relaxes
other usual assumptions like far-field approximation, spherical or plane wave
symmetry, TT gauge and source without internal interference. The string
solution is then adapted to give the radiation field of a transversal Alfven
wave in a rarefied plasma, where the tension is produced by an external static
magnetic field. Like for the string, the field strength turns out to be
independent from the frequency. We give a preliminary example of a numerical
solution based on parameters referred to Alfven waves in the solar corona.
Further astrophysical applications require an extension of the solution
procedure to second order in the amplitude, and consideration of border
effects. Future work will also address numerical and analytical near-field
solutions.
