Gravitational waves in general relativity. VI. The outgoing radiation condition

1961/11/21 by R. Sachs · 704 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Bounded function #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Euclidean geometry #General relativity #Geometry #Geophysics and Gravity Measurements #Gravitational field #Gravitational redshift #Gravitational wave #Lanczos tensor #Mathematical analysis #Mathematical physics #Mathematics #Metric tensor #Null (SQL) #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Quantum mechanics #Riemann curvature tensor #Tensor (intrinsic definition) #Weyl tensor

paper · doi:10.1098/rspa.1961.0202

published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 264(1318), 309-338 (Royal Society)

openalex publication_date 1961/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

Abstract A covariant formulation of the outgoing radiation condition for gravitational fields is proposed. The condition is based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor. It relates the absence of incoming radiation, in a gravitational field with bounded sources and Euclidean topology, to the asymptotic behaviour of the Riemann tensor. Fields that are algebraically special in the Petrov classification are highly special examples of fields obeying the suggested condition.

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