Are known maximal extensions of the Kerr and Kerr-Newman spacetimes physically meaningful and analytic?

TL;DR

This paper critically examines the maximal extensions of Kerr and Kerr-Newman spacetimes, arguing they are physically inconsistent and non-analytic, and proposes a new geometric interpretation that could lead to more physically meaningful models.

Contribution

The paper identifies issues with existing maximal extensions and offers a new geometric interpretation of key surfaces, suggesting a different approach for constructing analytic models.

Findings

Existing maximal extensions are physically inconsistent.

The surface r=0 is a dicone or a curved surface, not a disk.

A new geometric interpretation may enable more realistic models.

Abstract

In this paper we argue that the well-known maximal extensions of the Kerr and Kerr-Newman spacetimes characterized by a specific gluing (on disks) of two asymptotically flat regions with ADM masses of opposite signs are physically inconsistent and actually non-analytic. We also discover a correct geometrical interpretation of the surface $r=0$, $t={\rm const}$ - a dicone in the case of the Kerr solution and a more sophisticated surface of non-zero Gaussian curvature in the case of the Kerr-Newman solution - which suggests that the problem of constructing the maximal analytic extensions for these stationary spacetimes is likely to be performed within the models with only one asymptotically flat region, in which case a smooth crossing of the ring singularity becomes possible, for instance, after carrying out an appropriate transformation of the radial coordinate.