A gas turbine is provided including a rotor which includes a rotor portion of a fluid bearing for rotatably supporting the rotor, a radially outer stator portion, a radially inner stator portion including a stator portion of the fluid bearing, a compressor air passage extending between the radially outer stator portion and the radially inner stator portion, and an annular gap between the rotor and the radially inner stator portion partially forming an annular air passage in communication with the compressor air passage, wherein along a flow direction of air flowing within the annular air passage a radius of the air passage decreases in a first portion and then increases in a second portion. Further a method for operating a gas turbine is described.