Multipole expansions of the general-relativistic gravitational field of the external universe

Journal Article · Fri Aug 15 04:00:00 EDT 1986 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.34.991· OSTI ID:5567134

Zhang, X

The generic, vacuum, dynamical gravitational field in the vicinity of a freely falling observer is expanded in powers of distance away from the observer's spatial origin (i.e., in distance away from his timelike-geodesic world line). The expansion is determined fully, aside from coordinate freedom, by two families of time-dependent multipole moments: ''electric-type moments'' and ''magnetic-type moments'': which characterize the gravitational influence of the external universe. These ''external multipole moments'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives, evaluated on the observer's world line. The properties of these moments are discussed, and an analysis is given of the structure of the gravitational field's multipole expansion for the special case of de Donder coordinates. In de Donder coordinates the expansion involves only integral powers of distance from the origin; no logarithmic terms occur in this multiparameter expansion.

• Research Organization: Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125
• OSTI ID: 5567134
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 34:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
MULTIPOLES
NONLINEAR PROBLEMS
SERIES EXPANSION
SPHERICAL HARMONICS