Distributional energy momentum tensor of the extended Kerr geometry

TL;DR

This paper extends the energy-momentum tensor distribution analysis of the Kerr geometry into negative mass regions, addressing singularities and non-smoothness within a generalized Kerr-Schild framework.

Contribution

It introduces a generalized Kerr-Schild class that models the extended Kerr geometry, including negative mass regions, while handling singularities in a Colombeau-sense framework.

Findings

Extended Kerr geometry with negative mass regions modeled.

Singularities at branch surfaces are addressed within the generalized framework.

The geometry is associated with the maximally analytic Kerr-metric in a Colombeau sense.

Abstract

We generalize previous work on the energy-momentum tensor-distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr-Schild decomposition from one sheet to the double cover develops a singularity at the branch surface we have to take its non-smoothness into account. It is however possible to find a geometry within the generalized Kerr-Schild class that is in the Colombeau-sense associated to the maximally analytic Kerr-metric.