“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,” says Maximiliano Isi, a NASA Einstein Postdoctoral Fellow in MIT’s Kavli Institute for Astrophysics and Space Research and lead author of a study about a signal from a gravitational wave merger.
GW150914, reports MIT, was the first gravitational wave signal detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 from two inspiraling black holes that generated a new, ringing black hole. The coalescence released a huge amount of energy that rippled across space-time as gravitational waves confirming Hawking’s area theorem. “So, it’s not like you do this test once and it’s over. You do this once, and it’s the beginning,” observed Isi.
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 boundary beyond which nothing can ever escape according to general relativity — should never shrink. This law is Hawking’s area theorem, named after physicist Stephen Hawking, who derived the theorem in 1971.
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95% Confidence
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. In the new study, 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 percent 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 team plans 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.
Hawking’s Insights — Golden Age of the ’70s
In 1971, Stephen Hawking proposed the 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.
Thermal, Heat-emitting Objects—a Confounding Proposition
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,” Isi says. “The area law encapsulates a golden age in the ’70s where all these insights were being produced.”
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Hawking asks: “Could the Detection Confirm?”
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 Kip Thorne, the Feynman Professor of Theoretical Physics at Caltech. 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. It wasn’t until several years later, and the development of a technique by Isi and his colleagues, when testing the area law became feasible.
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A New Model –The Signal Before and After the Merger
In 2019, Isi and his colleagues developed a technique to extract the reverberations immediately following GW150914’s peak—the moment when the two parent black holes collided to form a new black hole. The team used the technique to pick out specific frequencies, or tones of the otherwise noisy aftermath, that they could use to calculate the final black hole’s mass and spin.
A black hole’s mass and spin are directly related to the area of its event horizon, and Thorne, recalling Hawking’s query, approached them with a follow-up: Could they use the same technique to compare the signal before and after the merger, and confirm the area theorem?
The researchers took on the challenge, and again split the GW150914 signal at its peak. They developed a model to analyze the signal before the peak, corresponding to the two inspiraling black holes, and to identify the mass and spin of both black holes before they merged. From these estimates, they calculated their total horizon areas—an estimate roughly equal to about 235,000 square kilometers, or roughly nine times the area of Massachusetts.
The “Ringdown”
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 spin, and ultimately its horizon area, which they found was equivalent to 367,000 square kilometers (approximately 13 times the area of Massachusetts).
“The data show with overwhelming confidence that the horizon area increased after the merger, and that the area law is satisfied with very high probability,” Isi says. “It was a relief that our result does agree with the paradigm that we expect, and does confirm our understanding of these complicated black hole mergers.”
“It’s encouraging that we can think in new, creative ways about gravitational-wave data, and reach questions we thought we couldn’t before,” Isi says. “We can keep teasing out pieces of information that speak directly to the pillars of what we think we understand. One day, this data may reveal something we didn’t expect.”
Undiscovered Exotic Objects May Not Be Bound By Hawking’s Law
“It is conceivable that the compact objects LIGO and Virgo observe are not exactly black holes as we expect them within Einstein’s theory,” wrote Max Isi in an email to The Daily Galaxy. “This may be either because the theory needs correction at some level (perhaps due to quantum gravity effects), or because there exist exotic “black hole mimickers”—that is, objects that look like black holes from a distance but do not have an event horizon as we expect (for example, a wormwhole, or a “gravastar”),” he continued.
“Either way,” Isi concluded, “the upshot is that these alternative objects would not necessarily be bound by Hawking’s area law. Therefore, experimentally probing this prediction with greater and greater precision might, some day, reveal the existence of physics beyond our current theories. Whatever the future holds, the area law is a cornerstone of our modern understanding of gravity and spacetime so, as scientists, we are beholden to check it against observation as best we can.”
Will Farr, a gravitational wave authority at Stony Brook University wrote in an email to The Daily Galaxy: “One thing we could see would be a final black hole from a merger that looks like a Kerr black hole (possesses only mass and angular momentum, but not electrical charge) but with an area that ends up smaller than the sum of the two progenitors. This is not allowed in General Relativity, and there are (tentative) arguments that *any* gravity theory would respect the area law, so it would be extra surprising. More generally, we could see something that looks like two black holes merging in the early phases of the signal, then something “wild” happens, and the late parts of the signal don’t look like a Kerr black hole at all. Of course, nobody expects this; but such an unexpected observation would make us rethink a lot of what we currently think we understand.”
Source: Testing the black-hole area law with GW150914, Physical Review Letters (2021). journals.aps.org/prl/accepted/ … 4336d883136eb53c122b
Maxwell Moe, astrophysicist, NASA Einstein Fellow, University of Arizona via Will Farr, Max Isi and Massachusetts Institute of Technology
Image credit: An artist’s illustration of two black holes merging. Image: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)
Maxwell Moe, astrophysicist, NASA Einstein Fellow, University of Arizona. Max can be found two nights a week probing the mysteries of the Universe at the Kitt Peak National Observatory. Max received his Ph.D in astronomy from Harvard University in 2015.
