A turbocharger for an internal combustion engine, the turbocharger being supported by hydrostatic bearings in both a radial and an axial direction by a compressed air supplied from a compressor of the turbocharger and boosted in pressure by a separate boost pump to a high enough pressure to support the rotor of the turbocharger. The turbocharger hydrostatic bearings are damped using wire mesh or dispersed friction dampers.