Linear responses of D0-branes via gauge/gravity correspondence

We study linear responses of D0-branes in the low frequency region by using gauge/gravity correspondence. The dynamics of the D0-branes is described by matrix theory with finite temperature, which is dual to a near extremal D0-brane black hole solution. We analyze the tensor mode and vector modes of a stress tensor and a Ramond-Ramond 1-form current of matrix theory. Then, we show that if a cutoff surface is close to a horizon of the D0-brane black hole, the linear responses take forms similar to the hydrodynamic stress tensor and current on S-8. By taking a Rindler limit, those linear responses come to obey the hydrodynamics exactly, which is consistent with previous works on a Rindler fluid. We also show that if the cutoff surface is far from the horizon, the linear responses do not take the forms of the hydrodynamic stress tensor and current on S-8. Especially, we find that the vector modes no longer possess a diffusion pole in the low frequency region, which indicates that the linear responses of the D0-branes cannot be explained by hydrodynamics.