Asymptotic flatness at spatial infinity in higher dimensions

Abstract

A definition of asymptotic flatness at spatial infinity in $d$ dimensions ($d\ge 4$) 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.

10 pages

References in corpus (5)

• Black Holes in Higher Dimensions
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Boundary Value Problem for Black Rings
• A Note on Conserved Charges of Asymptotically Flat and Anti-de Sitter Spaces in Arbitrary Dimensions

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• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• Cosmic branes and asymptotic structure
• Angular momentum at null infinity in higher dimensions
• Energy in higher-dimensional spacetimes
• On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
• Angular momentum at null infinity in five dimensions