Asymptotically flat space–times with one Killing vector field are studied. The Killing equations are solved asymptotically using polyhomogeneous expansions (i.e., series in powers of and and solved order by order. The solution to the leading terms of these expansions yields the asymptotic form of the Killing vector field. The possible classes of Killing fields are discussed by analyzing their orbits on null infinity. The integrability conditions of the Killing equations are used to obtain constraints on the components of the Weyl tensor and on the shear (σ). The behavior of the solutions to the constraint equations is studied. It is shown that for Killing fields that are non-supertranslational the characteristics of the constraint equations are the orbits of the restriction of the Killing field to null infinity. As an application, the particular case of boost-rotation symmetric space–times is considered. The constraints on are used to study the behavior of the coefficients that give rise to the Newman–Penrose constants, if the space–time is non-polyhomogeneous, or the logarithmic Newman–Penrose constants, if the space–time is polyhomogeneous.
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February 2000
Research Article|
February 01 2000
On Killing vector fields and Newman–Penrose constants
Juan Antonio Valiente Kroon
Juan Antonio Valiente Kroon
School of Mathematical Sciences, Queen Mary & Westfield College, Mile End Road, London E1 4NS, United Kingdom
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J. Math. Phys. 41, 898–923 (2000)
Article history
Received:
April 06 1999
Accepted:
September 17 1999
Citation
Juan Antonio Valiente Kroon; On Killing vector fields and Newman–Penrose constants. J. Math. Phys. 1 February 2000; 41 (2): 898–923. https://doi.org/10.1063/1.533170
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