The properties of large underdensities in the distribution of galaxies in the Universe, known as cosmic voids, are potentially sensitive probes of fundamental physics. We use data from the MultiDark suite of N-body simulations and multiple halo occupation distribution mocks to study the relationship between galaxy voids, identified using a watershed void-finding algorithm, and the gravitational potential $Phi$. We find that the majority of galaxy voids correspond to local density minima in larger-scale overdensities, and thus lie in potential wells. However, a subset of voids can be identified that closely trace maxima of the gravitational potential and thus stationary points of the velocity field. We identify a new void observable, $lambda_v$, which depends on a combination of the void size and the average galaxy density contrast within the void, and show that it provides a good proxy indicator of the potential at the void location. A simple linear scaling of $Phi$ as a function of $lambda_v$ is found to hold, independent of the redshift and properties of the galaxies used as tracers of voids. We provide an accurate fitting formula to describe the spherically averaged potential profile $Phi(r)$ about void centre locations. We discuss the importance of these results for the understanding of the evolution history of voids, and for their use in precision measurements of the integrated Sachs-Wolfe effect, gravitational lensing and peculiar velocity distortions in redshift space.
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