Asymptotic flatness at spatial infinity in higher dimensions

Details Asymptotic flatness at spatial infinity in higher dimensions Asymptotic flatness at spatial infinity in higher dimensions

2009-02-10

arxiv.org/abs/0902.1583v1

J.Math.Phys.50:072502,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages

Scientific paper

10.1063/1.3166141

A definition of asymptotic flatness at spatial infinity in $d$ dimensions ($d\geq 4$) is given using the conformal completion approach. Then we discuss asymptotic symmetry and conserved quantities. As in four dimensions, in $d$ dimensions we should impose a condition at spatial infinity that the "magnetic" part of the $d$-dimensional Weyl tensor vanishes at faster rate than the "electric" part does, in order to realize the Poincare symmetry as asymptotic symmetry and construct the conserved angular momentum. However, we found that an additional condition should be imposed in $d>4$ dimensions.

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