A definition of asymptotically Minkowskian space-times

Details A definition of asymptotically Minkowskian space-times A definition of asymptotically Minkowskian space-times

Aug 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979jmp....20.1731p&link_type=abstract

Journal of Mathematical Physics, Volume 20, Issue 8, pp. 1731-1740 (1979).

Mathematics

Mathematical Physics

15

Fundamental Problems And General Formalism

Scientific paper

A definition of asymptotic flatness is given without the use of Einstein's equations. For this we examine (a) the possible conditions on I+ and their consequences and relationships, and (b) the coordinate transformations which preserve certain forms of the unphysical metric g~ on a neighborhood of I+. Roughly, a space-time (M, g) is called asymptotically Minkowskian at future null infinity if it is weakly asymptotically simple, I+ is isometric to I+M (the I+ of the Minkowskian space-time) and (a) Ωμν=0, Ω-2ΩμΩμ=-1, C~λμρν=0 on I+ or, equivalently, (b) Ω-2ΩμΩμ=-1, Rμ ν=O (Ω2), Ω[λRμ] ν +ΩR[λ νμ]=O (Ω4) on I+. An equivalent definition is given based on the existence of a coordinate system in which, on a neighborhood of I+, g~ behaves as the conformal metric of Minkowski's space-time and can be written in an explicitly given form.

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