Figure 1: Left panel: A typical gravitational collapse. The portion of the event horizon at late times is isolated. Physically, one would expect the first law to apply to even though the entire space-time is not stationary because of the presence of gravitational radiation in the exterior region. Right panel: Space-time diagram of a black hole which is initially in equilibrium, absorbs a finite amount of radiation, and again settles down to equilibrium. Portions and of the horizon are isolated. One would expect the first law to hold on both portions although the space-time is not stationary.