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Vector perturbations can be decomposed into harmonic modes
of the Laplacian in the same manner as the scalars,

| |
(20) |

which satisfy a divergenceless condition
| |
(21) |

A
velocity field based on vector perturbations thus represents vorticity,
whereas scalar objects such as density perturbations are entirely
absent.
The corresponding symmetric tensor is constructed out of derivatives
as
| |
(22) |

A convenient representation is
| |
(23) |

Notice that and
.
Thus vector perturbations stimulate
the modes in the radiation.

*Wayne Hu*

*9/9/1997*