  The connection between spherical harmonics and symmetric tensors is explored.
For each spherical harmonic, a corresponding traceless symmetric tensor is
constructed. These tensors are then extended to include nonzero traces,
providing an orthonormal angular-momentum eigenbasis for symmetric tensors of
any rank. The relationship between the spherical-harmonic tensors and
spin-weighted spherical harmonics is derived. The results facilitate the
spherical-harmonic expansion of a large class of tensor-valued functions.
Several simple illustrative examples are discussed, and the formalism is used
to derive the leading-order effects of violations of Lorentz invariance in
Newtonian gravity.

Classical Physics