An Interior Solution for the Kerr Metric: A Novel Approach

TL;DR

This paper introduces a new interior solution for the Kerr metric using ellipsoidal coordinates, providing a more realistic model of rotating black hole interiors and analyzing their physical properties.

Contribution

It extends previous work by deriving a physically plausible interior solution for the Kerr metric through novel coordinate transformations.

Findings

The solution matches the Kerr exterior smoothly.

Energy conditions vary with rotation parameters.

The model exhibits anisotropic fluid properties.

Abstract

We present a novel approach for the construction of interior solutions for the Kerr metric, extending J. Ovalle's foundational work through ellipsoidal coordinate transformations. By deriving a physically plausible interior solution that smoothly matches the Kerr exterior metric, we analyze the energy conditions across various rotation parameters. Our findings reveal anisotropic fluid properties and energy condition behaviors in specific space-time regions, providing insights into the strong-field regime of rotating black holes. The proposed solution offers a more realistic description of rotating black hole interiors, with implications for understanding compact astrophysical objects.