On asymptotically flat algebraically special spacetimes in higher dimensions

Understand

We analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a "non-degenerate" geodetic multiple WAND.

• After imposing a fall-off condition necessary for asymptotic flatness, we determine the behaviour of the Weyl tensor as null infinity is approached along the WAND.
• This demonstrates that these spacetimes do not "peel-off" and do not contain gravitational radiation (in contrast to their four-dimensional counterparts).
• In the non-twisting case, the uniqueness of the Schwarzschild-Tangherlini metric is also proven.