Peeling of the Weyl tensor and gravitational radiation in higher dimensions

TL;DR

This work investigates how the Weyl tensor peels near null infinity in asymptotically flat spacetimes in dimensions $d>4$. Using Bondi coordinates and the higher-dimensional GHP/NP formalism, it derives that the leading term is algebraically type $N$, followed by type $II$, and then algebraically general type $G$, with a special extra type $N$ contribution in $d=5$ due to nonlinearities; for $d>5$ the next half-integer order terms cancel under standard decay of the Ricci tensor. A Bondi-energy flux formula is given in terms of the higher-dimensional Weyl components $oldsymbol{ extOmega}'_{ij}$, analogous to the 4D $oldsymbol{ extPsi}_4$ expression. The results differ qualitatively from 4D peeling and illuminate how dimensionality shapes asymptotic gravitational radiation and energy loss. The paper also clarifies the equivalence of conformal and Bondi definitions of asymptotic flatness for even dimensions and provides a route to computing Bondi flux directly from asymptotic Weyl data in higher dimensions.

Abstract

The peeling behaviour of the Weyl tensor near null infinity is determined for an asymptotically flat higher dimensional spacetime. The result is qualitatively different from the peeling property in 4d. To leading order, the Weyl tensor is type N. The first subleading term is type II. The next term is algebraically general in 6 or more dimensions but in 5 dimensions another type N term appears before the algebraically general term. The Bondi energy flux is written in terms of "Newman-Penrose" Weyl components.