Abstract
We determine the leading order falloff behavior of the Weyl tensor in higher-dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to ``expand'' in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the falloff rate of various Weyl components depends substantially on the chosen boundary conditions and is also influenced by the presence of a cosmological constant. The leading component is always algebraically special, but in various cases, it can be of type N, III, or II.
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