We analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a “nondegenerate” geodetic multiple Weyl aligned null direction. After imposing a fall-off condition necessary for asymptotic flatness, we determine the behavior of the Weyl tensor as null infinity is approached along the Weyl aligned null direction. This demonstrates that these spacetimes do not “peel off” and do not contain gravitational radiation (in contrast to their four-dimensional counterparts). In the nontwisting case, the uniqueness of the Schwarzschild-Tangherlini metric is also proven.

• Received 30 July 2009

DOI:https://doi.org/10.1103/PhysRevD.80.084041