A note on non-commutative dynamics of spinning D0 branes
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Rotational dynamics is known to polarize D0 branes into higher dimensional fuzzy D$p$-branes: the tension forces between D0 branes provide the centripetal acceleration, and a puffed up spinning configuration stabilizes. In this work, we consider a rotating cylindrical formation of finite height, wrapping a compact cycle of the background space along the axis of rotation. We find an intriguing relation between the angular speed, the geometry of the cylinder, and the scale of non-commutativity; and we point out a critical radius corresponding to the case where the area of the cylinder is proportional to the number of D0 branes - reminiscent of Matrix black holes.
20 pages, 1 figure, v2: typos corrected, citations added; v3: numerical analysis added, minor editing of discussion section; v4: citations added; v5: numerical analysis removed, final version
20 pages, 1 figure, v2: typos corrected, citations added; v3: numerical analysis added, minor editing of discussion section; v4: citations added; v5: numerical analysis removed, final version