Bonnor beam
1. History
2. Topology
The Bonnor beam has the topology $\mathbb{R}^4$.
3. Metrics and coordinates
On the range $r \in [0, r_0]$ $$ds^2 = -8\pi m r^2 du^2 - 2du dv + dr^2 + r^2 d\theta^2$$
On the range $r \in [r_0, +\infty]$
$$ds^2 = -8\pi m r_0^2 (1 + 2 \ln (\frac{r}{r_0})) du^2 - 2du dv + dr^2 + r^2 d\theta^2$$