Killing inequalities for relativistically rotating fluids

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Abstract
For rigidly rotating fluids in general relativity, it is shown that the angular momentum density is everywhere positive. This result depends on a global inequality satisfied by the Killing scalars. The inequality follows, via the Hopf theorem, from an elliptic equation (essentially one of the field equations) on the scalars. A derivation of the field equations in terms of the manifold of Killing orbits is presented. Possible generalizations of the result to systems with differential rotation or interior event horizons are discussed.

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