  The Helmholtz equation for symmetric, traceless, second-rank tensor fields in
three-dimensional flat space is solved in spherical and cylindrical coordinates
by separation of variables making use of the corresponding spin-weighted
harmonics. It is shown that any symmetric, traceless, divergenceless
second-rank tensor field that satisfies the Helmholtz equation can be expressed
in terms of two scalar potentials that satisfy the Helmholtz equation. Two such
expressions are given, which are adapted to the spherical or cylindrical
coordinates. The application to the linearized Einstein theory is discussed.
