Nonholonomic approach to rotating matter in general relativity

TL;DR

This paper introduces a nonholonomic framework to analyze differentially rotating matter in general relativity, extending previous methods limited to rigid rotation, and characterizes specific classes of rotating fluids including Schwarzschild and Kerr solutions.

Contribution

It generalizes the Ernst coordinate method using nonholonomic frames to handle differential rotation in matter distributions within general relativity.

Findings

Constructed a complex analytic tensor for matter states including Schwarzschild and Kerr.

Derived consistency relations for these matter classes.

Investigated properties of incompressible fluids within this framework.

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.