The Application of the Newman-Janis Algorithm in Obtaining Interior Solutions of the Kerr Metric

TL;DR

This paper demonstrates how the Newman-Janis algorithm can generate new interior solutions for the Kerr metric, enabling smooth matching of these solutions to the Kerr exterior, with potential applications in modeling rotating astrophysical objects.

Contribution

The paper introduces a method to produce physically acceptable interior solutions for the Kerr metric using the Newman-Janis algorithm, including boundary matching techniques.

Findings

New class of interior solutions generated via NJA

Smooth matching to Kerr exterior achieved

A trial solution with oblate spheroidal boundary surfaces presented

Abstract

In this paper we present a class of metrics to be considered as new possible sources for the Kerr metric. These new solutions are generated by applying the Newman-Janis algorithm (NJA) to any static spherically symmetric (SSS) ``seed'' metric. The continuity conditions for joining any two of these new metrics is presented. A specific analysis of the joining of interior solutions to the Kerr exterior is made. The boundary conditions used are those first developed by Dormois and Israel. We find that the NJA can be used to generate new physically allowable interior solutions. These new solutions can be matched smoothly to the Kerr metric. We present a general method for finding such solutions with oblate spheroidal boundary surfaces. Finally a trial solution is found and presented.