Evidence for a gravitational Myers effect

An indication for the existence of a collective Myers solution in the non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in fluctuations around the standard diagonal background. We show that this computation for non-abelian D0-branes in curved space has the geometric interpretation of computing the eigenvalues of the geodesic deviation operator for U(N)-valued coordinates. On general grounds one therefore expects a geometric Myers effect in regions of sufficiently negative curvature. We confirm this by explicit computations for non-abelian D0-branes on a sphere and a hyperboloid. For the former the diagonal solution is stable, but not so for the latter. We conclude by showing that near the horizon of a Schwarzschild black hole one also finds a tachyonic mode in the fluctuation spectrum, signaling the possibility of a near-horizon gravitationally induced Myers effect.