Asymptotic flatness at spatial infinity in higher dimensions

Understand

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.