Rotating Anisotropic Fluid Solutions

TL;DR

This paper introduces exact rotating anisotropic fluid solutions that satisfy energy conditions, match Kerr solutions on thin shells, and exhibit singularities similar to Kerr with additional features.

Contribution

It presents new exact rotating anisotropic fluid solutions satisfying energy conditions and matching Kerr solutions with specific singularity and surface properties.

Findings

Solutions satisfy all energy conditions for certain parameters

Solutions match Kerr extremal solution on thin shells

Solutions exhibit ring singularity and additional singularities

Abstract

An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the eigenvalues of this tensor and the energy-momentum tensor of the solutions are given explicitly. All have the ring singularity of Kerr's solution and in addition the solution one more singularity and some solutions of the family additional singularities.The solution matches to the extremal solution of Kerr on two surfaces, which are thin shells and for proper values of the parameters of the solution approximate oblate spheroids. One of these surfaces has positive surface density. The solutions of the family satisfy the matching conditions with the solution of Kerr on two pair of surfaces, which are again thin shells. The surface density of one pair of surfaces is given explicitly. Also for proper values of the parameters of the solutions the surfaces of the other pair approximate oblate spheroids.