  Cosmic voids in the large-scale structure of the Universe affect the peculiar
motions of objects in their vicinity. Although these motions are difficult to
observe directly, the clustering pattern of their surrounding tracers in
redshift space is influenced in a unique way. This allows to investigate the
interplay between densities and velocities around voids, which is solely
dictated by the laws of gravity. With the help of $N$-body simulations and
derived mock-galaxy catalogs we calculate the average density fluctuations
around voids identified with a watershed algorithm in redshift space and
compare the results with the expectation from general relativity and the
$\Lambda$CDM model. We find linear theory to work remarkably well in describing
the dynamics of voids. Adopting a Bayesian inference framework, we explore the
full posterior of our model parameters and forecast the achievable accuracy on
measurements of the growth rate of structure and the geometric distortion
through the Alcock-Paczynski effect. Systematic errors in the latter are
reduced from $\sim15\%$ to $\sim5\%$ when peculiar velocities are taken into
account. The relative parameter uncertainties in galaxy surveys with number
densities comparable to the SDSS MAIN (CMASS) sample probing a volume of
$1h^{-3}{\rm Gpc}^3$ yield $\sigma_{f/b}\left/(f/b)\right.\sim2\%$ ($20\%$) and
$\sigma_{D_AH}/D_AH\sim0.2\%$ ($2\%$), respectively. At this level of precision
the linear-theory model becomes systematics dominated, with parameter biases
that fall beyond these values. Nevertheless, the presented method is highly
model independent; its viability lies in the underlying assumption of
statistical isotropy of the Universe.
