  We have derived estimators for the linear growth rate of density fluctuations
using the cross-correlation function of voids and haloes in redshift space,
both directly and in Fourier form. In linear theory, this cross-correlation
contains only monopole and quadrupole terms. At scales greater than the void
radius, linear theory is a good match to voids traced out by haloes in N-body
simulations; small-scale random velocities are unimportant at these radii, only
tending to cause small and often negligible elongation of the redshift-space
cross-correlation function near its origin. By extracting the monopole and
quadrupole from the cross-correlation function, we measure the linear growth
rate without prior knowledge of the void profile or velocity dispersion. We
recover the linear growth parameter $\beta$ to 9% precision from an effective
volume of 3(Gpc/h)^3 using voids with radius greater than 25Mpc/h. Smaller
voids are predominantly sub-voids, which may be more sensitive to the random
velocity dispersion; they introduce noise and do not help to improve the
measurement. Adding velocity dispersion as a free parameter allows us to use
information at radii as small as half of the void radius. The precision on
$\beta$ is reduced to approximately 5%. Contrary to the simple redshift-space
distortion pattern in overdensities, voids show diverse shapes in redshift
space, and can appear either elongated or flattened along the line of sight.
This can be explained by the competing amplitudes of the local density
contrast, plus the radial velocity profile and its gradient, with the latter
two factors being determined by the cumulative density profile of voids. The
distortion pattern is therefore determined solely by the void profile and is
different for void-in-cloud and void-in-void. This diversity of redshift-space
void morphology complicates measurements of the Alcock-Paczynski effect using
voids.
