On the analyticity of stationary gravitational fields at spatial infinity
- 1 September 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (9) , 2006-2011
- https://doi.org/10.1063/1.525148
Abstract
It is proved that all stationary, vacuum solutions of Einstein’s equations which satisfy certain weak differentiability conditions characterizing asymptotic flatness, possess an analytic structure near spatial infinity. This analyticity theorem implies the existence of a multipole expansion whose coefficients can be expressed in terms of the Geroch–Hansen multipole moments defined at the point at infinity on the conformal manifold. This proves a longstanding conjecture that these moments uniquely determine the local structure of a stationary, asymptotically flat, vacuum metric.Keywords
This publication has 12 references indexed in Scilit:
- Multipole moments in general relativityJournal of Physics A: General Physics, 1979
- Multipole Moments of Electrostatic Space-TimesProgress of Theoretical Physics, 1976
- Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized BasisJournal of Mathematical Physics, 1971
- Static Axially Symmetric Gravitational FieldsPhysical Review D, 1970
- Multipole Moments. II. Curved SpaceJournal of Mathematical Physics, 1970
- On the analyticity of stationary vacuum solutions of Einstein's equationMathematical Proceedings of the Cambridge Philosophical Society, 1970
- On the analyticity of static vacuum solutions of Einstein's equationsMathematical Proceedings of the Cambridge Philosophical Society, 1970
- New Formulation of the Axially Symmetric Gravitational Field ProblemPhysical Review B, 1968
- Topology of Some Spheroidal MetricsJournal of Mathematical Physics, 1966
- On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the InteriorAmerican Journal of Mathematics, 1958