A hydrostatic air bearing in which a journal rotates within a cavity formed within a bearing race, and a sleeve that rotates with the journal within the cavity of the bearing race, where the sleeve is formed of a porous metallic material that allows for a bearing fluid such as air to flow from a high pressure side of the journal to a low pressure side of the journal through the porous sleeve that acts to dampen the bearing fluid flow, and therefore dampen the bearing. Another embodiment is for a hydrodynamic air bearing with an annular sleeve arranged between the rotating journal and the bearing race, where the annular sleeve is formed of a porous metallic material to dampen air flow across the journal.