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

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

2002-11-21

arxiv.org/abs/gr-qc/0211070v1

Class.Quant.Grav. 20 (2003) 1077-1102

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, no figures

Scientific paper

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.

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