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At the fundamental level, the 4-dimensional space-time of our direct experience might not be a continuum and discrete quantum entities might “collectively” rule its dynamics. Henceforth, it seems natural to think that in the “low-energy” regime some of its distinctive quantum attributes could, in principle, manifest themselves even at macroscopically large scales. Indeed, when confronted with Nature, classical gravitational dynamics of spinning astrophysical bodies is known to lead to paradoxes: to untangle them, dark matter or modifications to the classical law of gravity are openly considered. In this article, the hypothesis of a fluctuating space-time acquiring “at large distances” the properties of a Bose-Einstein condensate is pushed forward: firstly, it is shown that a natural outcome of this picture is the production of monopoles, dyons, and vortex lines of “quantized” gravitomagnetic—or gyrogravitational—flux along the transition phase; the minimal supported “charge” (and multiples of it) being directly linked with a nonzero (minimal) vacuum energy. Thus, a world of vibrating, spinning, interacting strings whose only elements in their construction are our topological concepts of space and time is envisioned, and they are proposed as tracers of the superfluid features of the space-time: the archetypal embodiment of these physical processes being set by the “gravitational roton”, an analogue of Landau’s classic higher-energy excitation used to explain the superfluid properties of helium II. The far and the near field asymptotics of string line solutions are presented and used to deduce their pair-interaction energy. Remarkably, it is found that two stationary, axis-aligned, quantum space-time vortices with the same sense of spin not only exhibit zones of repulsion but also of attraction, depending on their relative geodetic distance.