A new form of the Kerr solution

TL;DR

This paper introduces a novel form of the Kerr solution using a time coordinate aligned with free-falling observers, enhancing physical interpretability and mathematical properties near the horizon.

Contribution

It presents a new coordinate system for the Kerr solution that simplifies physical analysis and is compatible with the tetrad formalism, including a Hermitian Dirac Hamiltonian.

Findings

Coordinate system well-behaved at the horizon

Simplifies the Dirac Hamiltonian in Kerr spacetime

Enhances clarity of physical phenomena near black holes

Abstract

A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time coordinate. The chosen coordinates also ensure that the solution is well behaved at the horizon. The solution is well suited to the tetrad formalism and a convenient null tetrad is presented. The Dirac Hamiltonian in a Kerr background is also given and, for one choice of tetrad, it takes on a simple, Hermitian form.