A Possible Intuitive Derivation of the Kerr Metric in Orthogonal Form Based On Ellipsoidal Metric Ansatz

TL;DR

This paper presents an intuitive derivation of the Kerr metric using an orthogonal ellipsoidal metric ansatz, highlighting the geometric similarities with flat and Schwarzschild metrics in specific coordinate systems.

Contribution

It introduces a novel, physically motivated approach to derive the Kerr solution based on ellipsoidal symmetry and metric ansatz, offering clearer geometric insight.

Findings

Kerr metric can be derived from an orthogonal ellipsoidal metric ansatz.

The difference between Kerr and flat metrics lies in specific tensor components.

The approach simplifies understanding of Kerr geometry through coordinate transformations.

Abstract

In this paper we show that it is possible to derive the Kerr solution in an alternative, intuitive way, based on physical reasoning and starting from an orthogonal metric ansatz having manifest ellipsoidal space-time symmetry (ellipsoidal symmetry). This is possible because both flat metric in oblate spheroidal (ellipsoidal) coordinates and Kerr metric in Boyer-Lindquist coordinates can be rewritten in such a form that the difference between the two is only in the time-time and radial-radial metric tensor components, just as is the case with Schwarzschild metric and flat metric in spherical coordinates.