Interior Kerr solutions with the Newman-Janis algorithm starting with static physically reasonable space-times

TL;DR

This paper develops a method to generate Kerr interior solutions from static, physically reasonable space-times using the Newman-Janis algorithm, analyzing junction conditions, energy criteria, and applying it to various interior solutions.

Contribution

It introduces a straightforward approach to derive Kerr interior solutions from static solutions via the Newman-Janis algorithm, including new solutions with oblate spheroidal boundaries.

Findings

Derived Kerr interior solutions from Schwarzschild and Stewart solutions.

Analyzed junction conditions and energy conditions for the solutions.

Explored the slowly rotating limit of the solutions.

Abstract

We present a simple approach for obtaining Kerr interior solutions with the help of the Newman-Janis algorithm (NJA) starting with static space-times describing physically sensible interior Schwarzschild solutions. In this context, the Darmois-Israel (DI) junction conditions are analyzed. Starting from the incompressible Schwarzschild solution, a class of Kerr interior solutions is presented, together with a discussion of the slowly rotating limit. The energy conditions are discussed for the solutions so obtained. Finally, the NJA algorithm is applied to the static, anisotropic, conformally flat solutions found by Stewart leading to interior Kerr solutions with oblate spheroidal boundary surfaces.