New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields

TL;DR

This paper introduces a new framework for analyzing vacuum gravitational fields in stationary, axisymmetric systems, leading to a novel derivation of the Kerr solution and insights into the no-hair theorem.

Contribution

It develops a new method for solving vacuum Einstein equations in axisymmetric systems, simplifying the derivation of the Kerr solution and exploring its implications.

Findings

Successfully derived the Kerr solution from the new framework.

Provided techniques to simplify the analysis of axisymmetric vacuum fields.

Discussed implications for the no-hair theorem.

Abstract

A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting the Weyl tensor to type D produces a set of equations which can be solved, and a range of new techniques are introduced to simplify the problem. Imposing the further condition that the solution is asymptotically flat yields the Kerr solution uniquely. The implications of this result for the no-hair theorem are discussed. The techniques developed here have many other applications, which are described in the conclusions.