Signal-front gravidynamics of vector fields in the ray gauge

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Abstract
The dynamical evolution of a gravitating vector field (massive or massless) is analyzed along a signal-front coordinate (or null coordinate). Moreover, we specialize our frame of reference by adding the ray-gauge condition, which essentially consists of taking the affine parameter of the null geodesics contained in the signal-front hypersurfaces as the second kind of nonspatial coordinate. Then we extend previous results of Aragone and Chela-Flores to this matter-source case. We exhibit the algebraic and differential constraints for the present system, and the reduction process is accomplished. It is shown how the gravidynamics of the vector fields can be studied in terms of the minimum number of independent physical fields, half the usual timelike canonical first-order approach. It is found that the signal-front energy density is always non-negative. Moreover, the connection between vanishing signal energy fields and the Robinson-Trautman and Kundt plane radiative solutions is also shown. Finally, the limit of the matter signal energy, when the mass tends to zero, is shown to be (even in an arbitrary nonflat background) the sum of the related Maxwell signal energy plus the signal energy of a scalar massless field.

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