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.
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