On asymptotically flat algebraically special spacetimes in higher dimensions

TL;DR

This paper investigates the asymptotic structure of higher-dimensional vacuum spacetimes with special algebraic properties, showing they lack gravitational radiation and establishing the uniqueness of higher-dimensional Schwarzschild solutions.

Contribution

It provides a detailed analysis of asymptotic flatness and Weyl tensor behavior in higher dimensions, revealing differences from four-dimensional cases and proving uniqueness results.

Findings

Higher-dimensional algebraically special spacetimes do not exhibit peeling-off behavior.

These spacetimes do not contain gravitational radiation.

The Schwarzschild-Tangherlini metric is unique in the non-twisting case.

Abstract

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.