  Redshift space distortions within voids provide a unique method to test for
environmental dependence of the growth rate of structures in low density
regions, where effects of modified gravity theories might be important. We
derive a linear theory model for the redshift space void-galaxy correlation
that is valid at all pair separations, including deep within the void, and use
this to obtain expressions for the monopole $\xi^s_0$ and quadrupole $\xi^s_2$
contributions. Our derivation highlights terms that have previously been
neglected but are important within the void interior. As a result our model
differs from previous works and predicts new physical effects, including a
change in the sign of the quadrupole term within the void radius. We show how
the model can be generalised to include a velocity dispersion. We compare our
model predictions to measurements of the correlation function using mock void
and galaxy catalogues modelled after the BOSS CMASS galaxy sample using the Big
MultiDark $N$-body simulation, and show that the linear model with dispersion
provides an excellent fit to the data at all scales, $0\leq
s\leq120\;h^{-1}$Mpc. While the RSD model matches simulations, the linear bias
approximation does not hold within voids, and care is needed in fitting for the
growth rate. We show that fits to the redshift space correlation recover the
growth rate $f(z=0.52)$ to a precision of $2.7\%$ using the simulation volume
of $(2.5\;h^{-1}\mathrm{Gpc})^3$.
