A bit of everything

# Ellis-Bronnikov drainhole

The Ellis drainhole is the oldest example of a traversable wormhole. It's a class of spherically symmetric static spacetimes parametrized by $a$, the radius of the throat.

## 2. Topology

The Ellis-Bronnikov drainhole has the topology $\mathbb{R}^2 \times S^2$.

## 3. Metrics and coordinates

### Proper time coordinates

$$ds^2 = -dt^2 + dl^2 + (l^2 + a^2) (d\theta^2 + \sin^2 \theta d\varphi^2)$$