Rotating steady state configurations in general relativity

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Abstract
Spacetimes with axial and timelike Killing fields ημ and ξμ respectively are studied. A natural basis is constructed for the steady state configurations of matter with 4‐velocity uμ =αξμ+βημ. It is shown that the rate of shear tensor always has an eigenvector with zero eigenvalue lying in the 2‐space of Killing orbits. A natural coordinate system is constructed on the 2‐space of Killing orbits for rigidly rotating perfect matter. Gravitational isorotation is proved for the case of a perfect fluid with a one‐parameter equation of state. Locally nonrotating frames are constructed for purely stationary spacetimes.

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