English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give a general geometric definition of asymptotic flatness at null infinity in $d$-dimensional general relativity ($d$ even) within the framework of conformal infinity. Our definition is arrived at via an analysis of linear perturbations near null infinity and shown to be stable under such perturbations. The detailed fall off properties of the perturbations, as well as the gauge conditions that need to be imposed to make the perturbations regular at infinity, are qualitatively different in higher dimensions; in particular, the decay rate of a radiating solution at null infinity differs from that of a static solution in higher dimensions. The definition of asymptotic flatness in higher dimensions consequently also differs qualitatively from that in $d=4$. We then derive an expression for the generator conjugate to an asymptotic time translation symmetry for asymptotically flat spacetimes in $d$-dimensional general relativity ($d$ even) within the Hamiltonian framework, making use especially of a formalism developed by Wald and Zoupas. This generator is given by an integral over a cross section at null infinity of a certain local expression and is taken to be the definition of the Bondi energy in $d$ dimensions. Our definition yields a manifestly positive flux of radiated energy. Our definitions and constructions fail in odd spacetime dimensions, essentially because the regularity properties of the metric at null infinity seem to be insufficient in that case

Asymptotic flatness and Bondi energy in higher dimensional gravity