Structure of the gravitational field at spatial infinity. II. Asymptotically Minkowskian space--times

Journal Article · Mon Dec 31 23:00:00 EST 1979 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524338· OSTI ID:5725791

Persides, S

A new formulation is established for the study of the asymptotic structure at spatial infinity of asymptotically Minkowskian space--times. First, the concept of an asymptotically simple space--time at spatial infinity is defined. This is a (physical) space--time (M,g) which can be imbedded in an unphysical space--time (M,g) with a boundary S, a C/sup infinity/ metric g and a C/sup infinity/ scalar field ..cap omega.. such that ..cap omega..=0 on S, ..cap omega..>0 on M-S, and g/sup munu/ + g/sup mulambda/ g/sup nurho/ ..cap omega../sub vertical-barlambda/ ..cap omega../sub vertical-barrho/=..cap omega../sup -2/ g/sup murho/ +..cap omega../sup -4/ g/sup mulambda/ g/sup nurho/ ..cap omega../sub ;/lambda ..cap omega../sub ;/rho on M. Then an almost asymptotically flat space--time (AAFS) is defined as an asymptotically simple space--time for which S is isometric to the unit timelike hyperboloid and g/sup munu/ ..cap omega../sub vertical-barmu/ ..cap omega../sub vertical-barnu/ =..cap omega../sup -4/ g/sup munu/ ..cap omega../sub ;/..mu cap omega../sub ;/..nu..=-1 on S. Equivalent definitions are given in terms of the existence of coordinate systems in which g/sub munu/ or g/sub munu/ have simple explicitly given forms. The group of asymptotic symmetries of (M,g) is studied and is found to be isomorphic to the Lorentz group. The asymptotic behavior of an AAFS is studied. It is proven that the conformal metric g/sub munu/=..cap omega../sup 2/g/sub munu/ gives C/sup lambdamurhonu/=0, ..cap omega../sup -1/ C/sup lambdamurhonu/ ..cap omega../sub ;/..mu.. =0, ..cap omega../sup -2/ C/sup lambdamurhonu/ ..cap omega../sub ;/..mu.. ..cap omega../sub ;/..nu..=0 on S.

• Research Organization: Institute of Astronomy, University of Cambridge, Cambridge, England
• OSTI ID: 5725791
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:1; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
FOUR-DIMENSIONAL CALCULATIONS
GRAVITATIONAL FIELDS
MATHEMATICAL SPACE
METRICS
MINKOWSKI SPACE
SPACE