Nonholonomic approach to rotating matter in general relativity

Abstract

Rigidly rotating stationary matter in general relativity has been investigated by Kramer by the Ernst coordinate method. A weakness of this approach is that the Ernst potential does not exist for differential rotation. We now generalize the techniques by the use of a nonholonomic and nonrigid frame. We apply these techniques for differentially rotating perfect fluids. We construct a complex analytic tensor, characterizing the class of matter states in which both the interior Schwarzschild and the Kerr solution are contained. We derive consistency relations for this class of perfect fluids. We investigate incompressible fluids characterized by these tensors.