Air bearing to support a body

An air bearing has a rotor having a circularly curved radial rotor bearing surface along its circumferential direction. The air bearing also has a stator having at least one radial stator bearing surface partially enclosing the rotor in the circumferential direction. The radial stator bearing surface is curved according to a profile following the circumferential direction of the rotor and is fashioned to generate an air gap between it and the radial rotor bearing surface so that, upon operation, the rotor is borne, supported by an air current in the air gap. The profile shapes the air gap such that, at a starting temperature that deviates from an operating temperature, the air gap has a smaller thickness (measured in the radial direction) in a second region of the radial stator bearing surface in comparison to a first region of the radial stator bearing surface along the circumferential direction.