Anti-screening of the Galileon force around a disk center hole

The Vainshtein mechanism is known as an efficient way of screening the fifth force around a matter source in modified gravity. This has been verified mainly in highly symmetric matter configurations. To study how the Vainshtein mechanism works in a less symmetric setup, we numerically solve the scalar field equation around a disk with a hole at its center in the cubic Galileon theory. We find, surprisingly, that the Galileon force is enhanced, rather than suppressed, in the vicinity of the hole. This anti-screening effect is larger for a thinner, less massive disk with a smaller hole. At this stage our setup is only of academic interest and its astrophysical consequences are unclear, but this result implies that the Vainshtein screening mechanism around less symmetric matter configurations is quite nontrivial.