The eye of the storm: A regular Kerr black hole

TL;DR

This paper introduces a non-singular, rotating black hole model called the 'eye of the storm' that modifies Kerr geometry with a parameter controlling deviations, maintaining mathematical tractability and potential astrophysical observability.

Contribution

It proposes a new regular Kerr black hole solution with an asymptotically Minkowski core, preserving key symmetries and separability properties, and offers a tractable model for astrophysical tests.

Findings

The geometry satisfies some classical energy conditions.

Geodesic and Klein-Gordon equations are separable.

The model is highly tractable for astrophysical applications.

Abstract

We present a highly tractable non-singular modification of the Kerr geometry, dubbed the "eye of the storm" -- a rotating regular black hole with an asymptotically Minkowski core. This is achieved by "exponentially suppressing" the mass parameter in the Kerr spacetime: $m\to m \; e^{-\ell/r}$. The single parameter $\ell$ quantifies the deviation from the usual Kerr spacetime. Some of the classical energy conditions are globally satisfied, whilst certain choices for $\ell$ force any energy-condition-violating physics into the deep core. The geometry possesses the full "Killing tower'" of principal tensor, Killing--Yano tensor, and nontrivial Killing tensor, with associated Carter constant; hence the Hamilton--Jacobi equations are separable, and the geodesics integrable. The Klein--Gordon equation is also separable on this candidate spacetime. The tightly controlled deviation from Kerr renders the physics extraordinarily tractable when compared with analogous results in the current literature. This spacetime will be amenable to straightforward extraction of astrophysical observables falsifiable/ verifiable by the experimental community.