There are certain rules that even the most extreme objects in the universe must obey. A central law for black holes predicts that the area of their event horizons – the limit beyond which nothing can ever escape – should never shrink. This law is the Hawking Area Theorem, named after the physicist Stephen Hawking, who derived the theorem in 1971.
Fifty years later, physicists at MIT and elsewhere have now confirmed Hawking’s area theorem for the first time, using observations of gravitational waves. Their results appear today in Physical examination letters.
In the study, researchers take a closer look at GW150914, the first gravitational wave signal detected by the Laser Interferometer Gravitational-wave Observatory (LIGO), in 2015. The signal was the product of two inspiring black holes that generated a new black hole. , as well as a huge amount of energy that propagated through space-time in the form of gravitational waves.
If Hawking’s area theorem holds, then the area of the horizon of the new black hole should not be less than the total area of the horizon of its parent black holes. In the new study, physicists reanalyzed the GW150914 signal before and after the cosmic collision and found that indeed, the total area of the event horizon did not shrink after the merger – a result they report with 95% confidence.
Their findings mark the first direct observational confirmation of Hawking’s area theorem, which has been proven mathematically but has never been observed in nature until now. The team plans to test future gravitational wave signals to see if they could further confirm Hawking’s theorem or be a sign of new binding physics.
“It’s possible that there is a zoo of different compact objects, and although some of them are black holes that follow Einstein’s and Hawking’s laws, others may be slightly different beasts.” says lead author Maximiliano Isi, NASA postdoctoral researcher Einstein at MIT. Kavli Institute for Astrophysics and Space Research. “So it’s not like you take this test once and it’s over.” You do this once, and it’s the start.
Isi’s co-authors on the article are Will Farr of Stony Brook University and the Flatiron Institute’s Center for Computational Astrophysics, Matthew Giesler of Cornell University, Mark Scheel of Caltech, and Saul Teukolsky of University from Cornell and Caltech.
An era of intuitions
In 1971, Stephen Hawking proposed the area theorem, which sparked a series of fundamental ideas about the mechanics of black holes. The theorem predicts that the total area of the event horizon of a black hole – and all black holes in the universe, for that matter – should never decrease. The statement was a curious parallel to the Second Law of Thermodynamics, which states that entropy, or the degree of disorder in an object, should also never decrease.
The similarity between the two theories suggested that black holes could behave like thermal objects emitting heat – a baffling proposition, since black holes, by their very nature, were supposed to never let energy escape or shine. Hawking finally squared the two ideas in 1974, showing that black holes could have entropy and emit radiation over very long periods of time if their quantum effects were taken into account. This phenomenon has been dubbed “Hawking Radiation” and remains one of the most fundamental revelations about black holes.
“It all started with Hawking’s realization that the total area of the horizon in black holes can never decrease,” says Isi. “The regional law sums up a golden age in the 1970s when all these ideas were produced.”
Hawking and others have since shown that the area theorem works mathematically, but there was no way to verify it unnatural until the first detection of gravitational waves by LIGO.
Hawking, upon learning of the result, quickly contacted LIGO co-founder Kip Thorne, Feynman professor of theoretical physics at Caltech. His question: Could detection confirm the area theorem?
At the time, researchers did not have the ability to select the necessary information in the signal, before and after the merger, to determine whether the area of the final horizon had not shrunk, as Hawking’s theorem le would suppose. It was not until several years later, and the development of a technique by Isi and his colleagues, when the trial of zone law became possible.
Before and after
In 2019, Isi and her colleagues developed a technique to extract the reverberations immediately after the GW150914 peak – the moment the two parent black holes collided to form a new black hole. The team used the technique to select specific frequencies, or tones of otherwise noisy consequences, that they could use to calculate the mass and rotation of the final black hole.
The mass and spin of a black hole are directly related to the area of its event horizon, and Thorne, recalling Hawking’s request, approached them with a follow-up: could they use the same technique to compare the signal before and after fusion, and confirm the area theorem?
The researchers rose to the challenge and again split the GW150914 signal at its peak. They developed a model to analyze the pre-peak signal, corresponding to the two inspiring black holes, and to identify the mass and spin of the two black holes before they merge. From these estimates, they calculated the total area of their skyline – an estimate roughly equal to about 235,000 square kilometers, or about nine times the area of Massachusetts.
They then used their previous technique to extract the “ringdown”, or reverberations of the newly formed black hole, from which they calculated its mass and rotation, and ultimately its horizon area, which they found to be equivalent to 367 000 square kilometers (approximately 13 times the area of Bay State).
“The data shows with overwhelming confidence that the horizon area has increased after the merger and that the area law is satisfied with a very high probability,” Isi said. “It was a relief that our result dovetailed with the paradigm we expect and confirms our understanding of these complicated black hole mergers.”
The team plans to further test the Hawking’s Zone Theorem and other long-standing theories of black hole mechanics, using data from LIGO and Virgo, its counterpart in Italy.
“It’s encouraging to see that we can think in new and creative ways about gravitational wave data and answer questions that we thought we couldn’t before,” says Isi. “We can continue to extract information that directly relates to the pillars of what we think we understand. Someday, this data might reveal something we weren’t expecting.
This research was funded, in part, by NASA, the Simons Foundation, and the National Science Foundation.