Hawking’s black-hole area theorem, also known as the second law of black hole mechanics, states that the total horizon area of a classical black hole cannot decrease over time. The theorem is named after physicist Stephen Hawking, who proposed it in 1971. A team of U.S. physicists has now confirmed it for the first time, using observations of the gravitational-wave event GW150914.
In 1971, Stephen Hawking proposed the black-hole area theorem, which set off a series of fundamental insights about black hole mechanics.
The theorem predicts that the total area of a black hole’s event horizon — and all black holes in the Universe, for that matter — should never decrease. The statement was a curious parallel of the second law of thermodynamics, which states that the entropy, or degree of disorder within an object, should also never decrease.
The similarity between the two theories suggested that black holes could behave as thermal, heat-emitting objects — a confounding proposition, as black holes by their very nature were thought to never let energy escape, or radiate.
Hawking eventually squared the two ideas in 1974, showing that black holes could have entropy and emit radiation over very long timescales if their quantum effects were taken into account. This phenomenon was dubbed Hawking radiation and remains one of the most fundamental revelations about black holes.
“It all started with Hawking’s realization that the total horizon area in black holes can never go down,” said Dr. Maximiliano Isi, a physicist at MIT’s Kavli Institute for Astrophysics and Space Research.
“The area law encapsulates a golden age in the 1970s where all these insights were being produced.”
Hawking and others have since shown that the area theorem works out mathematically, but there had been no way to check it against nature until LIGO’s first detection of gravitational waves.
Hawking, on hearing of the result, quickly contacted LIGO co-founder Professor Kip Thorne. His question: Could the detection confirm the area theorem?
At the time, researchers did not have the ability to pick out the necessary information within the signal, before and after the merger, to determine whether the final horizon area did not decrease, as Hawking’s theorem would assume.
In the new study, Dr. Isi and his colleagues took a closer look at GW150914, the first gravitational wave signal detected by the Laser Interferometer Gravitational-wave Observatory (LIGO), in 2015.
The signal was a product of two inspiraling black holes that generated a new black hole, along with a huge amount of energy that rippled across space-time as gravitational waves.
If Hawking’s area theorem holds, then the horizon area of the new black hole should not be smaller than the total horizon area of its parent black holes.
The physicists reanalyzed the signal from GW150914 before and after the cosmic collision and found that indeed, the total event horizon area did not decrease after the merger — a result that they report with 95% confidence.
Their findings mark the first direct observational confirmation of Hawking’s area theorem, which has been proven mathematically but never observed in nature until now.
The researchers now plan to test future gravitational-wave signals to see if they might further confirm Hawking’s theorem or be a sign of new, law-bending physics.
“It is possible that there’s a zoo of different compact objects, and while some of them are the black holes that follow Einstein and Hawking’s laws, others may be slightly different beasts,” Dr. Isi said.
“So, it’s not like you do this test once and it’s over. You do this once, and it’s the beginning.”
The team’s paper will be published in the journal Physical Review Letters.
Maximiliano Isi et al. 2021. Testing the black-hole area law with GW150914. Physical Review Letters, in press; arXiv: 2012.04486
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