Non-commutative dynamics of spinning D0 branes

Rotational dynamics is known to polarize D0 branes into higher dimensional fuzzy Dp-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 a myriad of interesting results: an intriguing relation between the angular speed, the geometry of the cylinder, and the scale of noncommutativity; instabilities for small radii in relation to the height of the cylinder reminiscent of the Gregory-LaFlamme instability; and 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. The instabilities appear to lead to the lateral collapse of the cylinder into possibly a slinky configuration, akin to the Matrix string; or perhaps a Matrix black ring. 1 Duane [email protected] Address after September 2004: Cornell University 2 Kit [email protected] Address after September 2004: Cambridge University 3 [email protected]