Constructive proof of the Kerr-Newman black hole uniqueness including the extreme case

TL;DR

This paper presents a new constructive proof of the uniqueness of Kerr-Newman black holes, including extreme cases, using inverse scattering and Ernst potentials, advancing understanding of black hole solutions in general relativity.

Contribution

It introduces an explicit construction method for Kerr-Newman solutions that encompasses degenerate horizons, expanding previous uniqueness proofs.

Findings

Proves Kerr-Newman black hole uniqueness with a new constructive approach.

Extends the proof to include extreme (degenerate horizon) cases.

Utilizes inverse scattering method and Ernst potentials for the construction.

Abstract

A new proof of the uniqueness of the Kerr-Newman black hole solutions amongst asymptotically flat, stationary and axisymmetric electro-vacuum spacetimes surrounding a connected Killing horizon is given by means of an explicit construction of the corresponding complex Ernst potentials on the axis of symmetry. This construction, which makes use of the inverse scattering method, also works in the case of a degenerate horizon.