On Uniqueness of Kerr Space-time near null infinity

TL;DR

This paper proves that the Kerr metric is uniquely characterized as the only asymptotic flat, stationary, axial symmetric, Type-D vacuum solution near null infinity, using characteristic initial value problem techniques.

Contribution

It re-expresses the Kerr metric in Bondi-Sachs coordinates and establishes its uniqueness through a characteristic initial value problem approach.

Findings

Kerr metric expressed in Bondi-Sachs coordinates.

Proof of Kerr's uniqueness as a Type-D vacuum solution.

Calculation of N-P constants for Kerr space-time.

Abstract

We re-express the Kerr metric in standard Bondi-Saches' coordinate near null infinity ${\cal I}^+$. Using the uniqueness result of characteristic initial value problem, we prove the Kerr metric is the only asymptotic flat, stationary, axial symmetric, Type-D solution of vacuum Einstein equation. The Taylor series of Kerr space-time is expressed in terms of B-S coordinates and the N-P constants have been calculated.