The eye of the storm: a regular Kerr black hole

Abstract

We analyse in some detail 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 → m e-ℓ/r . The single suppression parameter ℓ quantifies the deviation from the usual Kerr spacetime. Some of the classical energy conditions are globally satisfied, whilst certain choices for ℓ 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. Both the Klein-Gordon equation and Maxwell's equations are also separable on this candidate spacetime. The tightly controlled deviation from Kerr renders the physics extraordinarily tractable when compared with analogous candidates in the literature. This spacetime will be amenable to straightforward extraction of astrophysical observables falsifiable/ verifiable by the experimental community.