Bondi mass cannot become negative in higher dimensions

Abstract

We prove that the Bondi mass of an asymptotically flat, vacuum, spacetime cannot become negative in any even dimension $d\ge 4$. The notion of Bondi mass is more subtle in $d>4$ dimensions because radiating metrics have a slower decay than stationary ones, and those subtleties are reflected by a considerably more difficult proof of positivity. Our proof holds for the standard spherical infinities, but also extends to infinities of more general type which are $(d-2)$-dimensional manifolds admitting a real Killing spinor. Such manifolds typically have special holonomy and Sasakian structures. The main technical advance of the paper is an expansion technique based on "conformal Gaussian null coordinates". This expansion helps us to understand the consequences imposed by Einstein's equations on the asymptotic tail of the metric field. As a by-product, we derive a coordinate expression for the geometrically invariant formula for the Bondi mass originally given by Hollands and Ishibashi.

19 pages, Latex, no figures, v2: Introduction partly reorganized, minor corrections

References in corpus (2)

• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• The Trautman-Bondi mass of initial data sets

Cited by in corpus (11)

• BMS Supertranslations and Memory in Four and Higher Dimensions
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Gravitational memory effects and Bondi-Metzner-Sachs symmetries in scalar-tensor theories
• Extensions of the asymptotic symmetry algebra of general relativity
• BMS-like symmetries in cosmology
• The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Symmetries, charges and conservation laws at causal diamonds in general relativity
• Instabilities of extremal rotating black holes in higher dimensions
• News vs Information
• Generalized BMS algebra in higher even dimensions