Vaidya
The Vaidya metric is the simple example of a radiating black hole, where the mass of the black hole is given as a function of time.
1. History
2. Topology
3. Metrics and coordinates
Outgoing metric :
$$ds^2 = -(1 - \frac{2 M(u)}{r}) du^2 - 2 du dr + r^2 (d\theta + \sin^2 \theta d\varphi^2)$$
Ingoing metric :
$$ds^2 = -(1 - \frac{2 M(v)}{r}) du^2 + 2 dv dr + r^2 (d\theta + \sin^2 \theta d\varphi^2)$$