HAWKING’S AREA THEOREM

When Stephen Hawking answered a similar question about black holes colliding in our December 1998 issue, he noted: “An interesting feature that I realized while I was getting into bed one night in 1970 is that the area of the event horizon, or boundary, of the final black hole has to be greater than the sum of the areas of the event horizons of the original black holes. This limits the amount of energy that can be radiated in gravitational waves and also suggested that the area of the event horizon is like the thermodynamic quantity entropy, a connection that was established when I later showed that black holes radiate like hot bodies.”

Called Hawking’s area theorem, this concept states that a black hole’s entropy — which is proportional to the area of its event horizon — cannot decrease. So, even if black holes can lose some small amount of mass during the merger, the final event horizon cannot have less area than the sum of the initial event horizons combined.

This theorem was developed some 45 years before the 2015 first detection of gravitational waves. A July 2021 paper in Physical Review Letters finally confirmed Hawking’s theorem observationally. In it, researchers reanalyzed the first gravitational-wave merger ever seen, called GW150914, and determined with 95 percent confidence that the area of the resulting black hole’s event horizon had not decreased compared to the event horizons of the progenitor black holes. — A.K.